With 2.1 update were added into game so called "Engineers", human (very likely) entities which can upgrade your ship equipment for a price. Price consist not only from needed input-components, but there is also mix of positive and negative changes to the properties of the upgraded equipment. Therefore is good to slow down, and thought twice or three times what upgrade type is the best for chosen component and a ship role, and whether is really needed the highest upgrade. Sometimes is for example much better take only upgrade lvl3, which have sufficiently high positive values and smaller negative, as go for upgrade lvl5 where you will have no use for so high positive value, but negatives will be higher for you all the time. Now is good to mention, that all this engineering is available only for these commanders, which have access to Horizons expansion pass, because all engineers (15 atm and 5ve more coming in 2.2) have bases on planet surfaces. I must say, that I like these new engineers bases, they have different/special atmosphere and look great ... exactly like it should be. Before I will continue, I want also note that all these places are "places of public interest" and therefore coming there in "Open" brings risk and possible encounters with unfriendly commander(s) ... but you can also find there friendly/lone souls and use those unexpected encounters for friendly chat and sometimes it can lead to future benefits/cooperation.
On the start you can get invitation from first five engineers (by public knowledge) if you have fulfilled basic "meeting" requirements (i.e. you have passed some minimal distance from start, have visited few times black marker and so on). When you have been invited, you can fle and dock at the engineer base and start process of getting engineer "unlocked". To get into engineer workshop, and start with upgrading, needs fulfilling engineer "unlock" requirements like can be commodities delivery, acquiring certain amount of bounties etc. After will be engineer unlocked you will have access to lvl1 upgrades. For access to higher lvls (5lvl is max) you will need improve your reputation with the given engineer, and this can be done with using his services (by doing upgrades, but without applying them) or in some cases exists also other ways (drop exploration data, trade to the engineer base, hand bounty vounchers). Now I will try explain how upgrading process works in general:
For upgrading equipment you need given input-components, which are micro-materials, data and special commodities. First two not need cargo space and are linked with commander (i.e. they are available for you all the time no matter what ship you are using), third needs cargo space and can be lost with ship destruction.
Micro-materials (76 different ones) can be obtained using different ways like combat, mining, surface searching, USS wrecks checking, doing missions etc. (except missions you will get 3! samples from each find micro-material or data described below) and you can have up to 1000 samples in inventory. Is good to say here that atm players found and is known how to get (or where) practically every micro-material. If you get some practice in this, you will learn that it is in reality much easier and need only small amount of time how it is and looks on start when you have no idea how all this works. Starting now with engineers is MUCH easier as it was in time when were they introduced. Yes, you may need (and it will make engineering much easier) use 3rd party sites (tools), but this is by design. Myself I do not have issues with this, imo it opens doors for creating gaming communities and things can be done different way and please therefore more ppl, some can see this as poor (very) game design and can have own well substantiated reasons ...
Data (30) can be obtained mostly by scanning things and it include ship wakes scanning, ships scanning, doing "raids" on surface installations data terminals, do missions etc.
Special commodities (26) can be mostly purchased (limited selling places) and/or acquired via missions (from bulletin boards). You can get those also from other players (opposite to previous two which cannot be shared between commanders).
Now let say that you have all needed input-components for upgrade and arrive to engineer base. For each upgrade you may need more different input-commodities, but always only one sample for one input commodity (i.e. 1x Sulphur, 1x Unexpected emission data and 1x power_converter). Upgrading process consist from two (three in weapons case) steps where first "roll" represents main changes to some given equipment properties within given intervals (positive but also negative), then comes bonus 2nd roll (smaller changes to random equipment properties) which can sometimes push result above/below limits given in first roll. For the weapons there is also chance get special ability, but about this latter. Especially 2nd roll values are "thing" which make some players crazy and let them crying very loudly how "stupid" all this engineering RNG is ... they "only" want asap the most SUPER result! ... reality is, that upgrading RNG works quite well with only first very few tries, unless you want get "special" 2nd roll which is (not a surprise) rare affair.
While playing I got one advice which I followed, and which I can heartedly recommend: Don't go after "super top" upgrade result right from start. This leads only to pure and absolutely terrible grind and can make you very easily pissed/frustrated when you will be unlucky (chances are high). To avoid frustration and have fun when doing "engineering" requires different approach. This approach is based on fact, that input-commodities are coming regularly to you as you are playing the game. When you will have more needed input-components, you can go to engineer and "try your luck". In majority of cases you still can reach decent improvement and sometimes you will hit a fortune and second bonuses will give you extra good results. The key here is, that you are not going to engineer primarily for the "super top" result. Small improvement is welcomed and you will have some free space in your inventory ... no frustration, smooth and diverse play, new encounters at the engineers bases (in open) etc ... it's not about stupid game design, it's about player own (...) chose/decision how to approach to the Engineers (imo).
Weapons, like was shortly mentioned earlier, can get also special ability (thing, where are atm in active beta ongoing big discussions about balancing with FDev like mainly "heat meta"). This special ability for sure is not small thing and your choice (you have more special abilities for chose, but can have applied only one per one weapon) can be quite important for your ship offensive strength. Access to this special ability is not difficult, because was given possibility sacrifice your reputation (1 or 2 lvls) with engineer for this (you can directly chose special ability which you want). This part works quite good, can be said that it's maybe too easy, but well ... it is how it is.
Now few those external sites which have all important details you may need:
And attached is picture where is listed how are linked different engineers (invitation for new engineers is usually coming when you are coming close to lvl4 upgrades access). Those in green (5ve) at bottom are newly coming in 2.2.
p.s.: I will continue further with telling the most useful upgrades, so you can concentrate only on acquiring limited amount from existing input-components. Don't forget, it need get some own practice before you realise how it works.