Seriously people, please stop coming to this thread saying "this not working baaah". Read the first post (and others), try things and continue trying things ! I mean, I wanted to get to the highest rank in federation but after three weeks of nothing I said it and went to explore some sights 1KLY away. E

Wasn't meant to be easy or fast. If you're tired of grinding reputation, maybe go Mining or something

If you're going to post here, please be it thanks to the OP because he helped you or constructive disccussion about current mecanism.
I'll state it again :
What is written can be false. Let's see why :
When you do a mission for Minor Faction (A), you get good reputation (+A) with them but might decrease reputation with their ennemies (--B). If "A" is aligned with a MAJOR Faction (Alliance, Empire or Federation) you get a
fraction of that good reputation with them (+MA). Important note : If "B" is allied with a MAJOR Faction you get decrease rep with that other MAJOR (--MB).
Now, because of that you might hit "Allied" Status with a MAJOR Faction without ever being Allied with MINOR Factions. Just proves you're friendly with a lots.
BUT. This also means that as soon as a MAJOR Power thinks you're an Ally,
every aligned Minor Faction will TREAT you AS an Ally . They will show green and maybe have "allied" next to their name in screens, but they're in fact NOT. They just give you the respect the higher ups ask them to give. Let's look at Federation : The feds like you, "the dukes of proxima centauri" (random name) are a federal minor faction... Friends of my boss are my friends. Capiche ? But who are you to the Dukes ? No one. Just a green card from fed space. If you want to get cozy in the dukes lounge, you gotta WORK for it. Oh and they'll tell the feds they like you... WHEN THEY DO !
So the fastest way to see where you're at with a faction is to take a random mission, do it and look at the reward charts. It will prompt your
REAL Reputation Standing.
Now Rank mission are triggered by three things : Reputation with the MAJOR Faction, Randomness, and
Reputation with a bunch of allied minor factions. It means that in my previous example, if both Minor are aligned with the same MAJOR, you are shooting yourself in the foot as you get "+MA and --MA". Remember
Reputation decreases faster than it increases !
It is important to note that exploring and trading contributes to reputation (don't know how) and space fights do too. Don't get caught smuggling illegal goods, accidental shots make you lose rep, and most of all DO NOT ATTACK GREEN SHIPS. If you want to rank up, don't try to cash in on bounties placed on your allies. (makes sense not to shoot allies when you think about it... my trail of righteousness might not have been liked by the higher ups...).
Every single mistep will cost you fifteen more steps to amend.
TL;DR : Get a faction aligned with the MAJOR Faction you want to get cozy with. Do a mission. Are you Allied at the end of that mission ? Yes ? good, ditch them and seek another Minor Faction to get cozy with. No ? Do missions until you're allied or until your eyes bleed (If your eyes start to bleed take time to think about your life choices). Only the mission reward screen can help you see your REAL Status. Rince and repeat to keep getting Allied with A LOT of Minor Factions. DO NOT DO ILLEGAL THINGS LIKE SHOOTING FRIENDS AND SMUGGLING. SMUGGLING IS BAD. SHOOTING FRIENDS IS FUN.
Eventually a rank up mission will pop out. (Some estimate it takes 15-20 minor factions being allied to you to get to highest rank)