Speed is the game's measurement of how fast you act. In the simplest terms possible, every 100 points of speed is equal to 1 movement per turn, so, say you have 400 speed, that means you act 4 times per turn.

A turn is game's basic measurement of time, each turn takes the same amount of time (there is an in-game clock, that measures time in-game, each turns takes the same amount of time on that clock), and everyone acts on the same turn, the turns are based on your actions, so a turn passes when you complete all of your actions.

It is important to note that most races have 100 base speed, of the playable chararcter, a few have over 100, but none have more than 180, and the snail have 40.

But what about values between 1 and 99? They are added until they complete 100, then you get 1 movement on that turn and the rest, if any, will be added to the next turn, So, for instance, if you 125 speed, you'll act once every turn plus once every 4 turns, this means you'll act 5 times every 4 turns.

In current stable patch, EA 23.188 Patch 2, mounting sets your speed to your mount's, so, say you have 100 speed and your mount have 125, when you mount it, it has enough strength and you have enough riding skill, YOUR speed will be set to 125. This means riding is the best skill in the game right now!

So, the VERY FIRST THING YOU MUST DO is go do 5 quests to get 5 platinum coins, whith those in hand go to the Tinker's Camp and learn the skill Riding, this is the most important skill ever!!! Just talk to the trainer there, it's simple, painless, quick.

Now that you have riding, you have to find a suitable mount, while you can mount anything, and I mean anything, some mounts are better than others, for instance, a human is better than a puppy, a horse is better than a human, and so on. There is no hard statistic to tell you which is best, just think "bigger = better". BUT there is a caviat: you want your mount to have as many fingers as possible!

I'll explain. Right now, the item that gives the most speed in the game is the Speed Ring, it comes in all shapes and from all materials, but all of them have something in common: they give at least 17 speed. This is very important!

But what can I mount? You can only mount your allies, so you'll have to recruit someone from your quest board at home or buy something to mount from a pet vendor or slaver. In Mysilia there is a pet vendor, you can buy horses from them, horses make a very good early mount, until you can get a more versatile mount. There is a slaver in Delphy, if you fancy that sort of thing.

Now we get to good part!

Now that you're mounted you should have noted that your speed is different, namely that it is less than your unmounted speed, that happens because your Riding skill is still weak, you'll need to run around a bit and gain experience on that to regain your former speed, but since you're probably mouting a horse, your speed will actually increase instead of just reaching 100 again. Once you reach ~30 in Riding, your speed will be set to your mount's speed. That is important, remember this for later!

And that is good and all, but we can do better!
For that you'll need the "Model Follower" feat at level 2, so grab that as soon as possible, and you'll need a "Lulwy Of Wind's Doujin Book". The doujin book is a bit tricky to get, I'm told that town festivals sell them, but I have only ever seen 2, and they weren't of Lulwy, it needs to be specifically of Lulwy, so to get that you'll need someone with the "painting" job/hobby working at your base, anyone is fine, just make sure to place down a shared box that accepts books, eventually they'll put a doujin there, just use any mage too identify it.

Have the doujin? Good, now save, unmount, grab the book by pressing R or the middle mouse button over it, click Grab, and then Gift is to your mount, your mount will read it, it doesn't matter if your mount is a horse and is illiterate, it will read it regardless, and if everything goes right, your mount will now be a devout follower of Lulwy of Wind! You can check that by trading with your mount, just press R or middle mouse button over it, click traid, in the Traits tab there should be a "Favor of the Wind" trait, which is what you want, if there isn't, reload and repeat the process.

Careful with doujins, though! They have charges like most other books, and if you use so much as 1 charge, regardless of how many it had, your mount will not change religion! So make sure to use a mage to indentify instead of using it yourself.

Now that your mount is a follower of Lulwy, its speed will grow with time, slowly, but surely, it will grow, so technically you now have an infinite scaling speed mount!

Remember that I said you want a mount with as many fingers as possible? Yeah, this is the time to talk about it.

As I've said before, each Speed Ring will give at least 17 speed, which is nice and dandy, but we can do better, oh so much better. An ether or spirit cloth ring can give up to 34 speed, which is very nice indeed.

But how do I get my horse to wear rings? It doesn't have fingers!
YET! It doesn't have fingers yet! For that you'll need a gene that gives fingers, I'll not write on how to get said genes because I have no clue how, you'll have to get lucky, but once you have genes that gives "Memory of finger", save them somewhere, go to Tinker's Camp and buy a Gene Machine, put on your base and start modifying your mount. Unmount first, click on the machine, select your mount, now click the machine again and select the gene with "Memory of finger", finally just wait until the process is done. Congratulations! Now your horse have a finger! Put a speed ring on it and the speed will increase! How cool is that!

Speed rings are a very rare drop, very rare blacksmith shop inventory, rare reward for beating adventurers on 1v1 and the target for wishes, which is the easiest way to get one or two.

Right now, without mods, you can get up to 3 fingers on your horse, so a max +102 speed for your horse from rings, but since horses have 190 base speed, we're talking 292 base speed, before Lulwy's buff and some other shenanigans, and that is a lot!

Now we have a Lulwy devout horse with 3 fingers, so how do we improve?

Remember that I've said you can mount anything? Yes, I mean it. The horse is pretty fast at 190, but not the fastest! Every character in the game, no matter how insignificant, falls into one of several races, and each race have a base speed, while horses have 190, gods have 200, catsisters have 280, metals have 300 and quicklings have a whopping 440.

440 is a LOT of speed. They act 4 times per turn plus once every 3 turns, so they act a total of 13 times every 3 turns. That is insane. And better yet, they start off with 2 fingers, meaning they can start off at a whopping 508 speed, before Lulwy's buff and other buffs... Put 3 fingers genes on your quickling and you're looking at 610 base speed before Lulwy's buff, with just a few days the Lulwy's buff should get you over 650 easily.

But wait! It gets better!
The "Lonely Soul" feat gives you up to 5% speed per empty slot in your party, so, say you have at least 50 charisma and you have the "Party Animal" feat at level 3, this gives you 8 party slots, if you fill just 1, that is, you are traveling just you and your mount, you'll have a whopping 35% bonus to speed, and it compounds with your mount's insanely high speed, that is, without Lulwy's buff, we're looking at 877 base speed! And after that, every Lulwy faith level will give between 2 and 3 speed, so the odds are when you get your quickling to 3 fingers you will have over 900 speed, which means you act 8 times before anyone does anything.

How cool is that?
Well... Not that cool. You see, quicklings are a problematic race because they only have 10 life... This means that they only get 1/10 of the HP provided by attributes. Sure, they are blinding fast, but if they face a gust of wind, they lose. Also, since they are a tiny race, they will need over 500 strength to carry you at top speed, and you yourself will need over 60 Riding skill to be able to handle such tiny mount...

So, is it worthy?
Kinda... 900 speed is nothing to scoff at, acting 9 times for each time everyone else acts is bonkers, in 9 actions you can feasibly kill most enemies, so you'll become basically invincible, but the down part is that you'll have to grind a lot for that 500 strength on the quickling and that 60 Riding skill.

Okay, so, what do you know about Ether Diseases?

I'll keep it simple: you WILL get an Ether Disease, no matter what, they are innevitable! But is it so bad? Well... It depends. Ether Diseases provide (or remove) attributes based on your base level, for instance, Scalding Face is an Ether Disease, it will REDUCE your charisma by 4+level/5, os it infinitely reduces your charisma, but not all Ether Diseases are negative!

Ether Wing is an Ether Disease that increases your speed by 10+level/5, and you can get it twice, meaning 20+2level/5! That's a lot of speed! Even better, your mount can get it too, which compounds with Lonely Soul to ludicrous amounts of speed!

But...
Like always, there's a catch... Because of course there is a catch.
All Ether Diseases are random, you cannot decide which you'll catch and while you have a moderate amount of control over when, you will constantly get new diseases that aren't as benefitial as Wings... This means you will have to constantly monitor your diseases and cure them as time goes on, while being very careful as to not cure too much and cure the wings.

Well, at least on your mount you have more control since they cannot get diseases nor progress diseases passively, like you do, so once you, somehow, get them sick with 2 wings, then you don't need to bother too much with them, just make sure they don't get too many of the bad ones.

While quicklings are the fastest, they aren't durable, but there are alternatives to that.

Demigods, when faithless, gain 1 speed every 10 days, so you can technically ride a faithless demigod and gain infinite speed over time, since with Lonely Soul you'll get 1.35 speed instead of 1, but the downside is that demigods are humanoids, they start at 100 base speed and you'll need that 60 Riding skill to handle them, but they do start with 2 fingers, which is nice, and they can use all types of equipment, so you can equip them head to toe with ether or spirit cloth material equips, each will give 5 speed each, so you'll have a 20~30 buffer from equips, plus ether equips aren't half bad with huge DV and at least a little PV. Plus demigod have 120 base life, which makes them very durable. You can also have a Lul'wy devout demigod, it will gain more faith than normal, but still at a lower pace than 1.35 per 10 days, you decide which is better for you.

Catsisters are another fast race, with 280 base speed, which is a lot, but they suffer from the quicklings lack of durability with only 25 base life. Sure, 1/4 of HP is better than 1/10, but it is still very fragile, and they don't start off with 55 DV like the quickling, so objectively the catsisters are an options, but not much better than the quickling. Catsisters are also tiny, so you need more Riding levels to deal with them.

Metals are a race of tanky monsters, like the bell, they have insanely low life, at only 1, so their HP will absolutely refuse to grow, BUT they have absurd resistances, being nearly impervious to most forms of damage, and the damage they do take is reduced by 99%, only lightining being a weakness. Also, like the horse, they don't have fingers, so ring speed will be capped at +102, not that that is bad, mind you, metals have 300 base speed, second highest. Still, at 1 life and near-immunity to damage, they are very brittle, so use at your risk. Metals are also pretty tiny, so bump that Riding up before mounting them.

So what should you mount?
Well... Whatever you want, really. I've seen people mount black cats, I, myself, mount Fiama, one of the NPCs that are at your base at the start of the game, you can mount a dinossaur, a dragon, a llama, it's really only dependent on how much you're willing to grind your mount's strength and your riding skill. Keep in mind that anything you do, even standing still, will very slowly give Riding skill experience, so you're always grinding that regardless of what you do.

Sure, quicklings make you so fast you basically become The Flash, but you'll need to tank everything yourself, learn taunt and take the damage for your mount, and even that won't stop it taking damage from AoE, so you WILL see your quickling faint a lot.

And, obviously, everything here is valid for current stable, which is EA 23.200. I don't know if this will change with newer versions, but if I'm playing I'll try to keep this up to date.

So, finally, SUMMARY!
Get riding skill from Tinker Camp, it costs 5 platinum coins; get a companion to mount, anything works, but a horse is a great start; grind a bit to get up to speed (literally, your speed at level 1 riding is BAD, you need at least 30 to be at your horse's top speed); use genes with Memory of Finger on your horse and give him Ring of Speed, as many as you physically can, plus, make sure every equipment on your horse is made of either Spirit Cloth or Ether; finally, gift your horse a Lulwy of Wind Doujin Book, so he worships the god of speed.
Yes, you can mount humans, I'm currently mounting Fiama, a unique NPC. Yes, a humanoid NPC with at least 125 base speed will be faster than a horse on the long run if you give it 2 rings of speed with at least 33 speed, becase 33x2=66, and 125+66=191, and 191>190, and will also use more equipment, making them more durable.
Get your mount, and maybe yourself, some Ether Wings disease, it increases speed infinitely based on your level. (though that can be hard...)

1.0 first, basic version
1.1 updated numbers with some findings in-game, will update more as I play and learn
1.2 (current) added Ether Disease section to increase speed even further