Faction wheel grinding for dummies

Press alt-F to see the factions, presumably you will know what you want your final faction to be. Give this number 1, we will number the rest 2 to 6 clockwise.

Start at number 3 and do only the AP missions there.
Then do the same for faction 4
Then the same for faction 5 (you may need to do some extra missions at 4, to get positive with 5).

Now find some npc's to kill for your opposite faction (which will be number 4). Spend a couple of hours grinding these until you have +60k faction (you will be about -60 to -80k when you start this) in your final faction choice (faction 1). At 60k rank your faction points gained for killing opposite drops from 150 a kill to 30, so it's time to stop this now. At this point you should have positive faction on your main faction and its 2 allies.

Do all your faction missions, then do your allies in whatever combination you require.

That's all there is to it.