This is a key element in the game the player must get a handle of as soon as possible, mainly because crafting is used to make upgrades for your exosuit, multi-tool and starship. Once again, the game does not teach you how to craft items at all at the beginning, so there will be a lot of blind fiddling involved just to figure out how things work. To craft an item or upgrade, click on an empty slot in your inventory then select the item/technology you create, before finally holding the craft button. Items can also be dismantled down to its basic components, then used to build other things.
Technology and upgrades typically require blueprints or recipes to build, with each one containing a list of materials required to craft the particular item. The more common components can usually be mined while you visit planets, while the rarer ones are initially only obtained through trade. So where can you find blueprints and recipes? Well there are two ways to get them primarily. One is through interacting with crashed pods during planet exploration; and two you can speak to aliens in shelters and space stations, then give the best answer from the dialogue tree that appears.
One other thing of note in regards to upgrades is that these typically come in four tiers. Starting from Sigma to Tau, to Theta and finally Omega. You don't have to build the lesser version of an upgrade to move on to the next tier though. Meaning, if you happen to the recipe and resources for the Omega version of a technology, you can just go ahead and build that even if you don't have the ones that come before it.