The recruitment gives you CR per month plus a bonus for each enemy fleet destroyed, i would think. LazyWizard knows these details better than me, so go ask him
Yeah, we need a way to explain this all in-game. Someone should bump that 'Codex Lore Section' suggestion thread.
You join a faction by buying the recruitment poster in their station (it currently doesn't have custom graphics, so it looks like a supply crate). You'll be inducted the next day if you meet the requirements (currently, only that you aren't enemies with that faction).
Once you have joined a faction, you will be paid at the start of each month. Your base salary is based on your current rank in that faction. Your bonus is calculated based on the relationship change with that faction's enemies (since there's no way to tell when you've killed an enemy fleet at the moment), and you can also receive penalties if you get into fights with your employer's allies. The paycheck message each month gives a detailed breakdown, so you'll know if you are doing something wrong.
Rank is currently calculated by lifetime bonus pay. I think you need to earn 10,000 * current rank, but I'd have to check the code. Max rank is 5, and the only bonuses rank grants at the moment are more pay and a very small boost to faction relationship. We are planning on expanding this to include restricting certain ships to higher ranks, but that didn't make it into this version.
One last thing, you can be kicked out of a faction if your relationship with them goes negative. Since there's currently no way to gain that favor back, it's permanent.