Quickest way I've found to ally with a faction is to hand in a lot of bounties at one time.
I went straight to allied with the Feds for handing in 1.2m. 600k immediately got me friendly with the Alliance.
This.
I have cleared up all my faction problems by bounty hunting at extraction sites. Outfit a viper (cheapest solution, cobra would work too), find an outpost allied with the faction of your choice that is orbiting a ringed planet. Nearby there will be extraction sites. Fly to one of these. You will find many system authority vessels, and miners. Eventually the bad guys will show up. Make sure they are wanted, and blow them out of the sky. The most efficient spawns are cobras imo. They're easy to dispatch and net between 5-25K average being somewhere around 10K.
Keep doing this until you run out of ammo or hit an innocent vessel. If that should happen you will become wanted and aquire a bounty. Don't worry it's affect on your faction is insignificant compared to the reward. Boost out of mass lock, with full power to engines, (couple of pips to shields), and hit supercruise. Fly back to that outpost you scouted earlier. This is why you wanted an outpost, and not a station (the station has a good chance of scanning you and destroying your ship and bounties). Pay off your bounty, and hand in your claims. You will get a significant rep boost directly with the major faction. And you will make about 600K per rep increase (unfriendly-neutral-friendly-allied).
For alliance faction you can do this in Leesti, at the Kolmogorov outpost.
In my opinion, this is the fastest and most profitable way to gain faction, and more importantly, the most fun (of course your opinion might differ if you don't enjoy combat). But even if you're not especially good at combat, the marks are easy in fully kitted Viper (which should be well within reach of any trader, or anyone who can afford the cost of all the alternative humanitarian route). You also get help from the local authorities, so it's pretty low risk. Just boost/supercruise out if you accidentally hit one of them.
The resource extraction sites are also some of the most fully realized areas in the game. The asteroids give you a real sense of space. You have strategic options available, such as hiding and luring opponents into mass lock, and you know exactly why you're there. You're teaming up with local authorities to defend miners and transports involved in mining operations. It's the closest thing to a living instance I have seen in this game, outside stations.
Hope this helps and you have as much fun gaining rep as I did!
. hunt in near anarchy sytems with a kw-scanner.
