1) ad revenue 2) virtual gifts for yourself and others 3) purchasing scarce resources (i.e. fuel in farmville)

The tricky part here is that a lot of the current darlings of Facebook games may not be as successful as they first appeared to be. There's a fair amount of evidence that the ad revenue is built on online scams, and those just aren't sustainable.

http://www.techcrunch.com/2009/10/31/scamville-the-social-gaming-ecosystem-of-hell/

All that aside, don't expect your first game to be a hit, or your fifth. You're going to have to try and fail before you come up with one that has traction.

From the top of my head I could think of two quite obvious answers:

1. Build a superb game, let people go wild about it and watch money coming in from ads

2. I played a few games where you could get bonuses, more ingame money, better weapons etc by clicking on partnerlinks or buying in a partnerhop using a personalized link. I would never give any money to something like that but the fact that WoW-swords are sold on eBay seems to prove the fact that such people exit ;)

(Third option would of course be the good old "Support the developers" Paypal-button ;)