The first thing you will want to do is gather up pebbles and stick/dead bushes so you can craft 4 stick blocks with 2x2 grid of sticks so you can do a 2x2 grid of stick blocks to make a hammer table.
Putting a pebble into your inventory turns it into a crafting stone, putting the crafting stone in the top of the hammer table and a pebble in the bottom, you can get flint, putting flint in the top left crafting grid slot and sticks in the top and bottom right gets you a flint hatchet which is a mini-axe to get you chopping logs!
After you get a flint hatchet, getting sticks is trivial and the then using flint in an actual crafting table, you can craft a flint pickaxe, a flint axe and a flint dagger. The flint axe is just a better flint hatchet that is actually better than stone!