Fight other ships via that mechanic (see: Combat). When defeated, they give you Hexantim, the currency of the game and the other two as well.
Spend Hexantim to buy blueprints for various types of modules as well as information (scan maps) to save yourself some trouble.
Scan or use the maps to locate the resources you need to build the blueprints.
Collect the resources. Resources are specific to different types of celestial bodies, and there are various mechanics here depending on what it is specifically.
Use the resources to build the module. This step will probably be straightforward, though it's likely to also cost either energy or time.
Install modules in the ship. The engineering here is somewhat complex, though at least you don't have to wire anything. Room types play a bigger role as far as strategy goes. Also various modifications you can make.
Fight maybe harder ships with your better modules.
All of this requires moving around the map via the Aphelion gtx0 module. Since this is an engineering game, movement will be upgradeable in various procedural ways.
