As one would expect, taming difficulty varies on the type of creature, as well as it's level. The following creatures are recommended for beginners, as they are fairly easy:
Dilophosaurus
Dodo Bird
Dimorphodon
Dilophosaurus
The Dilophosaurus is a Theropod dinosaur with a crest and a frill on and around it's head. Their body is covered in quil-like feathers, making it look fuzzy. They are about half the player's height, and they spit poison. They are also called Dilos for short.
The Dilophosaurus is a good companion to have, as they make good guards and hunting partners. They spit poison, which blinds their target, enabling you to subdue them safely.
Dodo Bird
The Dodo is a small, pudgy bird with a small head and a big beak. It has little ability to defend itself, and can't even fly.
Their is little reason to tame a Dodo bird, but if you have a mate-boosted pair, they produce a lot of eggs, which can be used for food, as well as in making kibble for taming. They also could serve as a distraction in battle for enemy carnivores.
Dimorphoodon
Dimorphodon is a small pterosaur about half the size of a Pteranodon. It is covered in feathers, and has a distinguishable long tail, which has a spade-shaped tip.
They make great surpise attackers, especially in swarms, where they can kill a rider and his steed with few to no casualties.

When searching for a pet, you need to know where to find them. Dodo birds are the easiest to find, as they spawn all over the island. Dilophosaurus is slightly harder to find, but they are still easier to search for. They spawn near medium to large sized bodies of water, such as a river or the coastline. Dimorphodon is the hardest of the three, found primarily in the swamp area, or large rivers farther inland.
To knock a creature unconcious, you need to do do at least one of these things:
Punch the living crap out of it
Shoot it with a slingshot
Use tranq arrows with a bow
or
Sting it while riding a Pulminoscorpius
Slingshot
To craft a slingshot, you need to be at least level 5. The engram costs 6 engram points. You will need 1xHide, 5xWood, and 20xFiber. For any new players, hide is collected from animals with an axe, wood is collected from a tree via punching or an axe, and fiber is collected from nearby plants with your hands or a metal sickle. You will need a plentiful supply of stones to use as ammunition.
Tranq arrows and bow
To craft a bow, you need to be at least level 15, and it costs 11 engram points. You will need 15xWood and 50xFiber.This requires arrows or tranq arrows for ammuniton. To craft a Tranq arrow you will need 1xArrow and 1xNarcotics. This requires level 20, with 8 engram points. Arrows require level 15 to craft, with 2 engram points. This requires 2xThatch, 2xFiber, and 1xFlint.
Narcotics
Narcotics are used to make tranq arrows, and are also used in the taming process. To craft this you need to be at least level 5 and have at least 6 engram points to spare. You will need 5xNarcoberries and1xSpoiled Meat. Narcoberries can be collected from nearby plants or from farming. Spoiled meat can be found if you don't cook meat before the spoil timer runs out. Raw meat spoils after 10 minutes. Narcotics are useful in that they provide the same effects of Narcoberries, but they don't spoil or decrease taming effectiveness.
Pulminoscorpius
This requires taming, so I won't go into this quite yet.

Capturing and taming
Catching a Dilophosaurus requires about 5-10 Punches, 2-3 Slingshot hits, or 2-5 tranq arrows. Catching a Dodo requires about 2-3 punches, 2-3 slingshot hits, or 1-2 tranq arrows. Catching a Dimorphodon requires about 1-5 tranq arrows.

After knocking a creature unconcious, you will be able to tame it. Taming is the most important step in this process, as it requires a lot of patience. You will need to put the food in the creature's inventory and then occasionally Taming varies on the level of the creature. Lower levels take less time, and higher levels take more time. This also changes the food requirements. You will also have to keep it's torpor up so that it stays unconcious long enough. You can develop your own taming strategy to increase your taming speed.
Dilophosaurus
Taming a Dilo can take 1-30 minutes depending on level or taming strategy.
Torpor
-You will need 20-120 Narcoberries.
or
-You will need 5-30 Narcotics.
Food
-You will need 10-25 raw meat.
You can also use prime meat, which can be harvested from Stegosaurus, T-Rex, Titanoboa, or other enormous dinosaurs.
Dodo Bird
Taming a Dodo bird can take 5-15 minutes depending on level or taming strategy.
Torpor
- 10-20 Narcoberries
or
- 2 or more Narcotics
Food
Dodo birds love Mejoberries, and will always eat them first before any berries.
- 10-30 Berries, espcially Mejoberries.
Make sure not to use Stimberries, as they will cause the Dodo to wake up faster.
Dimorphodon
Taming a Dimorphodon can take 10-30 minutes.
Torpor
-25-150 Narcotics (Dimorphodon won't eat Narcoberries)
Food
-25-60 Raw meat

Now that you've tamed your critter, you're given the option to name them. If you can't think of a name, don't worry, I'll provide you with a plethora of names to choose from.
Dilophosaurus
-Diny
-Snapper
-Fluffy
-Dennis
-Ozzie
-Rip Van Winkle
-Liz
-Lizzy
-Charmander
-Sal
-Spitter
-Chompy
-Chomps
-Nibbler
Dodo Bird
-Bird Brain
-Doddy
-Breakfast
-Lunch
-Dinner
-Stupid Turkey
-A balanced breakfast
-The Annihilator
-Stormageddon
-The Dark Lord
-Dodo Unit No.(Number)
-Egg slave
Dimorphodon
-Sqawks
-Pterry
-Petry
-FeatherHead
-Donny
-Sting
-Winged Death