When you first begin the game, start gathering resources with your bare fists by punching trees for wood and coconuts, picking up stone, and foraging for things such as thatch and rope and berries in small trees. The berries will be plenty sufficient when it comes to eating, at least for quite awhile. Whenever your character is thirsty, jump in the water and you will refill your water meter immediately due to drinking while you swim. Hit the shade whenever your character is hot, or build a campfire whenever your character gets cold.
Leveling up should always be your goal. The way to earn experience points is to either gather resources or craft items. To complete the level up, wait for the notification that you have a level to use, then go to the stat boost screen and start picking what you want to boost. Initially, health, speed and weight are good because weight lets you carry more stuff, speed lets you run away from threats faster, and weight allows you to carry more goods in your pack.
Once you gain a level, you get engram points, which can then be spent on the ability to craft new items. Each row of craftable goods is unlocked whenever you gain another level. Unlock based on your needs, but in general, try to unlock everything. You're going to need everything at some point or another. Clothes keep you warm and defend you from attacks, for example, while weapons make for faster harvesting and easier dinosaur killing, and shelter-related stuff keeps you out of the elements.
To craft many items at the same time, you want to go to the crafting menu, long tap the item icon, and then when the slider appears, drag it to the number that you want. Since you are going to need loads of walls and other hut related items to build a hut (or multiple huts), this is especially useful for shelter related stuff. Use it when you're constructing fragile but powerful weapons, as well, or arrows for your bow.
Taming dinosaurs is a major component of the game. You can tame with or without combat - passive tames are easier to pull off while active tames are tougher. Typically, you will need to tranquilize it, which can be done with narcotics (made from spoiled meat and mejoberries using a mortar and pestle), or if you are at a higher level, you can use tranquilizer arrows to make the job a hell of a lot easier.