I strongly recommend
inara. It'd be a nightmare keeping track of stuff without it. If you're playing on PC, I'd also recommend
ED Market Connector. It's an app that syncs your inventory with the Inara site, so you can see how many upgrades you can craft and what you need for the next grade etc.
Generally, once you gain access to an Engineer and unlock them (see the inara link for how to unlock each engineer), then you can start crafting. By and large you gain rep by crafting modules, and with some engineers there are other methods - selling commodities or exploration data at their station. This lets you climb up the Engineer grades/rep.
If you're Engineering a new (previously un-Engineered) item, you have to go up through the grades
for that piece of equipment each time. Need to Engineer five multi-cannons? That's 5 times Grade 1..5. If you have modules Engineered via the old system, it lets you start at one grade lower (i.e. if you had a thruster upgraded to G5 in the old system, you can immediately do a G4 upgrade, you don't have to start again at 1.
You don't exactly have to complete one device grade to get to the next. You can generally skip onto the next grade once you're about (not sure exactly) 1/2 or 2/3 way to the next grade. It's your choice then if you complete the current grade or skip onto the next one.
The Materials Traders are a god-send. If you discover any "Very Rare" materials out there, scoop them up. Even if you don't need those ones, the higher grade materials are very good for exchanging. Also, target ships everywhere you go and scan them as they pass. Doesn't cost you any time, but you get a lot of data materials.
