When you create a new world, you will have a female and a male creature. They will be named by default 'Eve' and 'Adam'.

As your very first action, breed Adam & Eve. (Do not worry about traits, etc. right now. That will be covered later in this guide.)
You do so by hovering over the '...' under Adam/Eve and then click the heart. Make sure Eve has a fat belly, then move her into a nest.

<-- Breeding button
<-- A pregnant animal
What do I do with Adam now?
Then, make Adam collect berries from a berry bush. How to do so is almost like mating; hover over the '...' under the bush, then click the button with the Paw holding a Fruit. Click it as many times as it will allow.
The green ovals on Eve and Adam's chest are their energy for the day. Every action, moving, mating, attacking, collecting berries, etc. takes one energy.
Now what?
Now press your space bar or the sundown button at the top of the screen.
Sleeping will refill Eve and Adam's energy ovals.
Make SURE Eve is in a nest at night, or she won't give birth!

WARNING: If Eve's child had a red or green blob pop up over it, it is sick! More about staying healthy later.
Again, send out Adam to collect berries. Hunting comes later in this guide. Make sure Adam or Eve has a energy left and are next to each other. (Move Eve from the nest and either next to Adam, or to a different nest with Adam by it.)
Mate Adam and Eve again. If no other nests are availible, have Eve collect berries for the day until out of energy. Same with Adam. If all berries are picked, use Adam's energy to go to the next berry bush. Put Eve by the nest with her baby.
Eve's baby will be able to move out of the nest, making room for Eve's next child. If berries are in reach of her nest, have her collect them. Have Adam collect berries.
Eve has had another baby! Repeat day 2's actions. Have the older baby collect berries if possible.
I won't bore you with saying what to do every day. Here are my tips for daily actions.
~Mate your animals as much and as often as possible. You MUST have 10+ pack members for your species to survive.
~Collect berries and stay away from Bearyenas for your first 'Week' or so until you have enough animals to help with hunting and fighting.
~Stay on the starter island until this guide recommends you move. So stay on your current island for now, or your animals will likely die.

Moles:
With moles, make sure to stay behind them. They turn direction after every move you make. Try and make sure you have enough energy left to kill them. You can collect the food the next day or send someone with energy to collect it if needed.
Rabbits
Rabbits may be a little harder, since they can actually move. Like moles, they move around after every turn you take. Try to sneak up on them.
Fishing
You must have an animal with the webbed paw ability. If it has the fish ability (Icon has a fish on it), then the animal can catch fish. If it only has webbed paw, it can collect algae for a lot of nesting material. If it has webbed paw and cracking, it can harvest clams.
<--This albino has webbed paw and fishing abilities.
Make the animal go over to the water and swim around. You'll likely see schools of fish. If your animal is less than 1 tile from the fish, click the fish icon to catch the fish for food.
Note: Do NOT harvest from the green things with the orange spikes, or you will get hurt.

Basic Fighting Controls:
Fighting is like mating and collecting berries. Click the '...' under the animal you wish to fight, then click the claw mark button. If it's not a Nichling, you can simply click the claw mark button without the '...'. You have attacked.
Fighting your own kind:
You can fight strays of your own kind if you want. (Or spend 5 food to get them to join your pack- more on why you should later- or mate with them. There's a very low chance of them spending the night in a nest if female to birth it.) You can either drive them away or kill them. Some will fight back, some will flee you. You do not get any food from killing them, just another skeleton. Lick your packmates if they got a bleed effect to cure the bleeding. Just click the '...' below them and then click the licking icon. Make sure the animal that's going to lick it is right next to it, not above or diagonal to it.
Fighting Bearyenas:
Bearyenas are on of the hardest things you can fight. If one appears, gather your strongest fighters (More on how to tell later.) and go over to the Bearyena.
Then attack. Again, if any packmates get a bleed effect, have one lick them by pressing the '...' and then clicking the lick icon.
Note: The smaller, brighter colored Bearyenas are "Friandly Bearyenas" and won't attack while wandering through your pack.

You may be asking: Now what? I've explored my whole island and I have no more goals or challenges. Consider travelling to another island!
When you finally feel ready to leave the starter island, with a pack of about 10, do this.
Go over to the closest area that has a tile with an odd pointy rock on it, it will be on an ocean edge of your island. It will either have pink flowers or dirt and bones around it.

Travelling rock tile and area, dirt-and-bone style.
Bring your pack over to be on the area by the rock tile. (The area for your pack is circled in teal in the picture) Use the closest animal to the rock tile (Rock tile circled in green in the picture) to click the travel button that will be on the rock tile. It looks like a palm tree.

Make sure you have a LOT of food. I recomend at least 100 food for a pack of 10-15. I recomend your packs not be greater in size than 10, or you may struggle to find food. Make sure you have enough material for at least one nest.
This pack is ready to travel.

First, make sure you are not in a swamp. If so, move on to the closest gray tile ASAP and travel somewhere else. Why? because swamps have disease!
I don't know a whole lot about other islands, but here is what to do when you arrive.
Find a source of food.
Make a nest. You must continue to keep your pack in shape by having children! Making a nest cost nesting material, you must have 10 for 1 nest. Clear away some grass to find some (sometimes you won't find any), or collect algae. But hopefully you went prepared.
Expand your territory in search of rescourses. Food is a big problem when travelling. Make sure you are safe. Make more nests. Have more children. Your pack should be stable again in a few game days.
You can move islands as many times as you like, whenever you like. If you don't like the next island you arrive on, you can repeat the process of moving to the rock tile and travel to a differant island.

Oh, no! Your newborn has a red or greed blob icon flash over it. Panic hits! What to do?
Since you can't move a newborn away, move the rest of your pack away! (I recommend clearing another area for the pack to move to in advance)
When you can move the sick baby, move it away from your pack's direction.
Once the sick animal is far away, the pack may come back to camp, breed, harvest, and hunt again safely.
When the sick animal dies, your world is safe for now until the next diseased baby is born. No disease remains on its bones.
Make sure your animals, when you mate them, have two differant immunity genes. For example, an A immunity animal can mate with a K immunity animal safely. But, unless you want sick babies, never mate animals of the same immunity, like a C immunity with a C immunity. That will result in an extremely high chance of the baby being born sick, to never be healthy.
Note: Animals born sick will never cure, but animals that got infected from another animal will cure after a few game days.
Some sick animals
I recomend this distance away from the healthy animals as a minimum.

Loners- the Nichlings who appear randomly at your pack area. You might attack them, you might ignore them. But do you give them 5 food to join your pack? You should. Check their immunity gene. If it's one not found in your pack, invite them to join, even if their abilities aren't good.

Why? Sometimes, your pack will interbreed so much that every animal has the same immunity gene, which causes sickness in the baby if two of the same immunity gene mate. A loner can bring a new immunity gene into the pack to effectively help prevent that from happening!

Yeah, it's possible, and it's always how my packs die out. Their numbers get too large. A good pack will keep its numbers between 10 to a maximum of 15. Otherwise, problems happen.

~Deciding who to breed with who becomes a huge headache
~Newborns are being born sick pretty consistantly, even though you bred with different immnunity genes
~Animals are being born consistantly with almost the same abilities
~You are having a hard time finding and collecting enough food

There are only two ways to fix this common problem.
One is to start banishing animals that have bad abilities or have the same general abilities of another animal, and getting loners with different abilities and immunitys to join the pack. Try to keep your pack's members unique, if they all start to have the same general ablilties, banish all of the similar ones but keep 1-2 of the animals that have those abilities.
The second choice is to travel to another island. You can either bring your whole pack or not. Either way works, many animals will starve at the new island while trying to find food scources and the pack will naturally shrink to a manageable size.

This pack of 19 is stuggling with being too successful. In the photo below they are migrating to a rock tile so they can go to a new island.

Don't worry, it's not very hard to learn!
Genetics will determine what the animal looks like, what it can do, and how strong it is. First, let's start with explaining the GUI for genetics.
The A, B, or C indicates the animal's rank. A, or Alpha, get the food when there's not enough for everyone. B, or Beta, come next and some get food if there's enough. If there's enough for everyone but the last in line, C, or Omega, the Omega won't get to eat.
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Every animal has different abilities. This one has webbed paw, attack, digging and fishing. If an animal doesn't have an ability, the icon will not be on its list and it will have a "low chance of succeeding" if you make it do that action.
Starting in order, the paw print means Speed. That means how far an animal can go in one turn.
Next, the webbed paw means it can breathe underwater and swim.
The digging paw means how well it can dig for food
The claw marks are damage. This animal has 4 damage, pretty good.
Now, in the second row things get a bit more complicated.
Under the paw print shows how high its fertility is. If your animal does not have this, it's infertile.
The shield is its immunity.
The eye is eyesight, which is how far an animal can see (Like in tall grass).
The face is hearing, how far it can hear prey.
The nose is smelling, how far it can smell berries and prey.
The leg is stealth.
The nose sniffing an animal is how scentless the animal is, good for hunting.
The snowflake is how well it does with cold.
The sun is how well it does with heat.
The second menu shows fur color, horn color, etc. It's not as important, it shows what body part types they have, fur color & pattern, horns, etc. I'm not going to list them all, because there's a lot and, in-game, you can hover over the icon to get a decent idea of what that icon means.
Albino animal genes v.s regular genes.

The mutation menu allows you to, basically, add in genes not in the mother or father's gene pool. You can also add ones that are in their gene pool for a greater chance of getting those two genes in the child.

Click the button circled in red. Then select a circle on the DNA strand that says 50% under it.
A large menu will pop up.

Select a gene from the menu, then click the check mark on the right edge of the selection menu.
You have now selected a gene that has a chance of appearing in the animal's future offspring.

Have too many animals to keep track of? Getting a headache from trying to figure out who to breed with who? Well, the Family Tree is your solution!
The family tree shows all alive animals, and a few recently dead ones.
You can sort by genes and abilities to figure out who to breed who with. It also shows the full list of gene traits (the DNA strand table)
Click the button circled in red while an animal is selected.

Here's a photo guide I made to explain the very basics of how it looks when you select an animal.
To sort by gene/ability, select the blank circle at the bottom.
Either one, gene or ability, depending on what you want to sort by.
Then select a gene or ability. For ABILITYS, each animal's icon will have a number. If it's a 0, they don't have the ability you sorted by.
Here I sorted by the digging ability. If the animal has a 0, it doesn't have the ability. If it has over a one, it has a higher, better level of the ability.
For GENES, I sorted by spiky body. Only one on my visible tree has had it. That animal's icon is bright blue. Its decendants are colored a dark blue, which means the trait is in them but it is inactive.