So, if you have just arrived on the ports, you may have noticed that the port hexagons can't have nests on. This is just encouragement to move on forward! You should use up your day exploring the island. If you're lucky, you can find a berry bush early. Your island is pretty small, so you will probably find a good base. If you have cracking ability, then you should set up a "camp" near a tree, but if you have good berry picking ability, then you should set up a "camp" near a berry bush.
So, what do I mean by a "camp"?
I mean set up some nests using a pregnant female (which, at this point at time, will probably be Eve.)
It's best to keep the nest right next to a place where your Eve can harvest. If your Eve has no harvesting abilities at all (even 1 can do!), then your camp should be in an area with a lot of berry bushes, as children that inherited Adam's runner legs can pick berries around you as you expand your tribe.
Here's a screenshot example of how your island may look like when you start out:

A few days in, you probably have a lot of grown-up children and nobody healthy to breed them with.
Use a good fighter - at this point, having Adam's poison fangs can be gamechanging - and make them explore around, making sure to use your smelling and hearing ability. What we're looking for is a wanderer, just like Eve. A wanderer will carry new genetics for your children to breed into the tribe.
Sometimes, they can be on the edge of the island, but at others they can be right next to your base. They move around by themselves, so they can be difficult to catch. Make sure that you have enough food to feed your tribe and 6+ extra. If you don't, wait until you have enough to allow the wanderer to move in without causing any starvation.
Now, what might your wanderer look like?
Well, anything really!
It can change your tribe forever... some genes are only unlocked through finding a wanderer with them. Here's an image of what a possible wanderer may be, from my very first game:

Pay attention to the wanderer's age, as if they are old like mine is, they aren't worth inviting. Just breed with them, get out the genes they carry, and leave them die alone. You can use the extra food during droughts.
How would my tribe be if I didn't invite wanderers? Well, here's an image of part of my tribe.
Notice that there are 2 strange creatures amongst them. In the next section, I will describe some creatures you may encounter among the way.

Now, another thing you need to pay attention to is the IMMUNITY GENES.
In story mode, you will want to keep Home Island immunity for the goal island: ADAM'S ISLAND.
But what else is there to immunity genes?
If you breed creatures that have similar immunity genes, such as a female with G - I and a male with I - F, then they have a chance of passing on two I genes to their baby, making them ill. You need to keep the baby distanced from the rest of the tribe, as it can pass on sickness. Sickness damages you every day you have it (creatures with same immunity genes will have it for their whole life). When it passes on, you will get a little notification on the side. This will last a few days on a healthy nicheling, and can cause a little reduction in lifespan.
So, this makes incest VERY bad to do... ONLY breed those with similar immunity genes if there's no other choice (e.g brink of extinction).
Now, you need to breed with the wanderer at any opportunity (as long as no immunity genes are shared) so your family can continue onwards, as Adam and Eve will die very soon, Eve going first.
You NEED to have a good amount of both males and females in the tribe, but having less males is better than less females as those males can breed with the females.

Bearyenas
Bearyenas are the main predators of the world of Niche. On your first island, you won't encounter many. I spent a LOT of time on that island, and only ever encountered 2.
They will damage you at night, and can be killers. If your nicheling starts bleeding from an attack, you can lick them to help that, and healing fruits can take off that damage. Purring using a purr snout (one that looks like a cat face) can also help this. The best way to deal with a Bearyena is to swarm them, and attack with any creature possible, even if they have bad attacks. When you kill a Bearyena, they will turn into a pile of meat, which is equivalent to 10 food.
Friendly Bearyenas
"Wait, so there's a friendly version of a predator?" Yes!
Sometimes, an evil Bearyena will spawn with a little baby following it. Once you kill the mother, you can tame the baby using 3 food. This Bearyena will be friendly, and never attack you.
The screenshot I showed with the "strange creatures" depicts 2 friendly Bearyenas in our camp.
These Bearyenas look a little different to the evil ones, so you can easily distinguish them.
When they are an adult, you can breed a female with them (as all Friendly Bearyenas are male). You can get special genetics out of this.
These genetics are (and correct me if I miss any out!):

• Bearyena Snout
  
• Bearyena Claw
  
• Bearyena Hind Legs
  
• Bearyena Ears

When you get these in an ACTIVE slot, you unlock them in your mutation menu.
Having a double Bearyena Claw and the Bearyena Hind Legs will make it difficult for your nicheling to move.
Killer Bearyenas
More difficult than normal Bearyenas, killers to weak nichelings.
Bluebirds
For now, bluebirds aren't a worry. Only on the next island will they begin spawning.
What they do is steal meat left on the ground (e.g hunted bunny meat) and also can take babies that are left alone... so if you have that sickly baby, at least 1 adult must stay near them so they aren't taken away.
Here's an image of some bluebirds in the skies on your next island:

These aren't too bad, but if you move around a lot and often leave babies alone, they are exactly what will ruin your tribe.
Rogue Males
These males look like wanderers, have terrible genes such as no paws, identical immunity genes, derp snout and haemophilia.
They will target your females and breed unwillingly with them.
To deter them, you must attack them, preferably poisoning them.
Here's an image that includes a rogue male:

Bears (all types)
Friendly bears
These bears won't harm you, and can be payed nesting material to watch your babies to stop the bluebirds.
Defender bears
These bears will attack you if you attack anything else.
Basically the protector of all nature.
Balance bears
These aren't a worry at this time, but once you reach the mountains, they will SWARM YOU
and are absolute MONSTERS.
You need very strong creatures to keep your base protected from these.
Arctic Ram Foxes
These only appear on the mountains, along with the Balance Bears. They often spawn in packs, and usually aren't too big of a worry unless you have a nicheling wandering alone.
Dodomingos
These... absolute... IDIOTS... will steal your nests... constantly... and attract creatures when attacked... and drop like no food...
There's nothing more about them.
Just the literal troll of Niche.
Apes (all types)
Hearing apes
These apes will find you by hearing. Having velvet paws and avoiding sticks is the only way to stop them from finding you.
Seeing apes
These apes will find you from seeing. They are less likely to come to you if you have distasteful appearance (e.g bearyena snout)
Smelling apes
These apes will find you by smelling. They are less likely to come to you if you have distasteful scent (e.g stinky tail)

As well as annoying or evil creatures, there's also food to catch and grab.
Fish
To get these, you need a good fishing ability. The swarms of fish are a very reliable food source. As well as this, natural fish types (like clown koi) are also good food, but it's best to wait until they die naturally (as over time, they age too!)
Bunnies
To get these, you need to be able to attack.
The best technique is to pounce onto the hexagon where they currently are, they will leap onto one next to you and you can then swipe them. If you have high enough strength you can one-hit them and not worry about a chase, but if you do need to chase it's not worth it. They give 3 food.
Stagmoles
To get these, you need to attack them without them seeing you. They turn around clockwise each time you use a gem, so using the right tactics you can easily pounce them. They give 4 food.
Normal Berries
To get these, you need some sort of berry-picking ability, which you can view in your abilities tab or in the family tree. The level of the skill reflects how many berries you can pick at once. If there is a drought, less berries will regrow. When it rains, all berries regrow and the berry is put back into it's normal state.
Poison Berries
To get these, you need a berry-picking ability and an active poison-inflicting trait (or else these berries will poison you and can be catastrophic). They work the same as normal berries except for the poisonous part.
Walrus Deers
To get these, you have to be in the mountains. They are difficult to kill, due to moving so much, but offer great meat rewards. I sadly don't know how much they drop.
Crabbits
To get these, you need to attack them from behind. Since they usually take a few hits to kill, it's best to wait until they perish, then you often can get a feast with a bunch of them being dead. I sadly don't know how much they drop.
Nuts
To get these, you need a cracking ability to get it from the floor. You can also crack nuts from the tops of trees with a winged creature. The floor nuts give 2 food and the tree nuts give 1 food.
Cacti
To get these, you pick them like a berry bush, but they will prickle and hurt you without good enough defence. The food is just like the berries.
Termite hills
To get these, you must crack them open before harvesting. There are two types of these hills: harmless and angered. Harmless has no special effect, and angered will give whoever touches it termites, which damage you per day. These do rebuild after an amount of time, and can be the opposite to what they used to be. You need to have the bug harvesting ability to pick from these successfully, and the higher it is the more you can pick at a time. It eventually runs out, just like berry bushes.
Stinky plants
To get these, you harvest them like a normal berry bush. When you do harvest them, their juice will get all over your nicheling, and it is especially attractive to smelling apes. The best harvesting technique is to have 2 nichelings, who will lick the juice off each other once they picked all they can.
Carnivorous plants
To get these, you need to slice it open and collect the fruit. But be warned: if in smell vision it appears RED, it will eat your nicheling, and you will need to use another to release it! So make sure to only be near those that are GREEN in smell vision,
Enemies
When you kill any enemy, they drop food. The enemies were listed in the section above.

If I missed any, then please inform me in the comments. I am trying my best to assist people.

After a lot of time, you will probably be considering moving to a new island. Take FERTILE creatures, as you need to regain your family once you move once more. Make sure you bring at least one strong nicheling (I brought my strongest), the best mover, the best gatherer (nutcracking and berry picking is good) and any others you favour (like ones that carry good genes). Make sure you have a surplus of food, as you can starve early into the next island when you come unprepared. Once you move, you just repeat this process of expanding, but this time breeding in genes which will come in useful in future.
Here are some genes you will want, the basics of what they do is explained in them.:

• Big ears (heat resistance)
  
• Lean body (heat resistance)
  
• Wings (bat or normal) (most possible movement)
  
• Big body (+damage and cold resistance)
  
• Poison fangs (poisons creatures upon attack, allows harvest of poison berries)
  
• Scorpion tail (poisons creatures upon attack, allows harvest of poison berries)
  
• Toxic body (poisons creatures upon attack, allows harvest of poison berries)
  
• Nimble fingers (allows cracking & berry picking)
  
• Cracker jaw (allows cracking)
  
• Bat head (efficient bug collection)
  
• Gills (allows breathing underwater)

From now on, you can work out everything on your own.
If I missed anything out, or you have more questions, then just tell me.
See you!