Once you have found the ideal location you can begin to construct your base. To do this you will need to use the Fabricator to craft the Habitat Builder. Before you can operate the Habitat Builder you will require a computer chip and a battery (computer chips are made with 1 quartz, 1 silver, and 2 jeweled disk piece and a battery is made with 1 copper and 3 acid mushrooms). Once you have these you will be able to press RMB to open and close the Habitat building menu which will have a number of tabs (Base Pieces, Exterior Modules, Interior Pieces, Interior Modules and Miscellaneous) which will enable you to craft tunnels and utility items.
To build these items however will require specific amounts of materials which you look for and collect. When you have the necessary materials you need to design your layout and put down a foundation by placing the outline of the structure you want to build in position and then select the 'Building' option to consume the materials. If you have already crafted a scanner you will be able to use it around any wreckages and abandoned bases to help you find new blueprints which you can then use to upgrade your base.