The great thing about FB advertising is that it's easy to test out campaigns before scaling up. Plus, they display your ads NOW and charge you LATER.
If you find a good affiliate deal that you want to promote, simply test out a couple ads and angles using FB. Usually tying in with an existing fan page works best.
You should be able to spot your winners after spending only around $10-20. Only thing you NEVER want to do is link directly to an affiliate offer. These days, FB will pretty much nuke your ad almost instantly if you do that. And if you're a repeat offender, they'll shut down your ad account. So figure out a good strategy to give value, provide your visitor with something that will make them happy somehow, THEN monetize them either via mail, an additional link, or via retargeting.
Hope this helps!
Tony