How to Understand Engineering?
If you Shift+Right Arrow, Q to the leftmost tab, then look at the bottom right of the UI there’s an Engineers panel I think. Open that up and it should list the engineers you’ve heard about and you can look at each of their entries to see what the next step is to get into their good graces. When you do, they’ll share with you contact information for other engineers.
The short explanation is they want things, you provide those things and in return they’ll give you access to their engineering facilities that let you trade materials (non-cargo inventory items) to ‘roll’ an improvement of a particular type on a stored instance of a module of a module class specific to the type of improvements offered.
The higher the grade of rolling you attempt to do (there are 5 levels of engineering upgrade for most things), the higher the quantity and level (rarity) of the mats required to do a single improvement crafting roll on a module. Initially you complete their task to unlock their workshop, after which you need to use the crafting options on modules to improve your standing with the engineer up to grade 5 access. This isn’t time limited, it’s material limited, so if you go prepared with a loaded inventory of materials you can max out access in one visit after you unlock the workshop.
It’s basically standard gameplay except not as directly profitable. Instead of getting paid in credits, you get paid in the potential to push your ship module performance far, far beyond stock performance.
You can also sort of like, ‘bookmark’ a single engineering workshop improvement crafting option for each engineer, I believe. This is important because otherwise you can’t access workshop engineering options without being at a given engineer’s workshop, which is a physical landing pad somewhere in the galaxy. If you want to be able to workshop remotely, you need to pick and choose the upgrades wisely.
Basically, it pays to go to your engineer workshops prepared to get most everything done in one go, so you might look into material farming first.