I keep trying to punch the trees, but I never get any wood or branches. How am I supposed to play this game?
You can or better have to pick them from the ground until you have a hatchet to chop down trees.
On the ground? I have been looking for hours. I am in the jungle does that matter?
Yes and no 
At least along side the river you should be able to to see them easier.
At the starter area ( so called “Noob river”) they are all around but they are every where in every biome to find. Some times they are harder to see. So check the coast line of the river.
the branches may look like white roots on the ground. Somewhat harder to spot among the grasses of the jungle. As mentioned, try looking along the river or in clearings.
Also need plant fiber to turn into twine, and rocks.
usually around beach areas on noob River. 5 will make a hatchet, then you will get more. But be warned around level 30, you will be drowning in branches lol.
I dump my plethora of sticks into the dryer to make dry wood. Helps a bit.
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