Crafting goes hand in hand with structure building. In Adventure Mode, you will start out with nothing, and will have to take down trees and break rocks in order to begin obtaining crafting items, such as logs and stones. Anytime a crafting item is picked up, you can go into the inventory screen and all the possible craftable objects that can be created from that item will appear. Hovering over an object with your mouse will make the recipe and stats of that object pop up. If a craftable object's picture is solid, you can create that object. However, if an object's picture is semi-transparent, you will still need to gather the appropriate resources as stated by the recipe in order to fully craft the object.
Raw Materials are gathered by hitting the object enough times with either your bare fists (right mouse button without anything equipped), which will take a while; or with the Axe, which will take considerably less time. The stronger the material, the more hits it will take to break the object apart.