Credits: Chu O' Fee
First steps
You can't do anything without wood. Now you can't just collect all the wood with your hand and turn it into planks. First, you've got to create tools to do it. Start by finding Gravel and collecting Flint, because that's what's going to be the base for the tools. Turn your Flint into Flint Shard on a crafting grid.
Getting wood
Start by beating the leaves and bushes to get some sticks; sometimes you can even find them laying on the ground. With a Flint shard and a Stick, create your first tool - a Knife. Now go cut some grass or other plants to get the fibers.
Make an Axe
Now that you have Sticks, Flint, and Fibers, you can craft an Axe and come much closer to creating planks. Strip a Log and put it on the Chopping Log (made by putting a Wood Log into the Crafting grid). Use an axe on a Stripped log and you've got yourself planks. From that point on forward, you are capable of crafting so many more items.