Crafting is the very heart of Terraria. You need to catch resources and build gear and items if you want to explore your world. Getting resources is easy, as for many of them you just need to kill enemies, use your tools to knock down trees, and dig tunnels to find ores.
Crafting can be a little more confusing if you are new to the game. First, you will need to open up your main menu. On PC, this is done by hitting the escape button. In the bottom left corner, you will see a list of items you can make. The list will consist of everything you can build with the resources you currently have. This will be small when you start, but one of those items will be a workbench. To craft an item, just double click on it. If you want to learn what you need to build something, just click on it once and the different resources you need will pop up.
If you build this, you will access to more recipes, including simple weapons and armors. As long as you are near the workbench, and have the right resources, you will be able to build any recipe unlocked by that workbench.
The game is filled with different items that will allow you to craft new items. Some can be made as furniture, while others need to be found, or purchased from NPCs. As you play through the game, you will find all manner of items that help you craft and new resources to build new items from.