I don't market Amazon, but from listening to others it's pretty much the review/content site model. Create content that reviews the products you're promoting, or have general content about a subject and related Amazon products as advertisements on your site. Then play the SEO game. It's all going to boil down to traffic to your site in the end.
Or implement the amazon products on your website. Then this way you can promtoe your page everywhere on the internet.
The Amazon program seems exciting at first because you have so many products at your disposal. The problem is, they pay VERY LOW COMMISSIONS! I put together an Amazon site several years back, and even when it drove traffic, it made hardly any commissions (in comparison to my other affiliate websites). If you want to make a decent income from affiliate marketing I wouldn't suggest using the Amazon program. I'm sure there are a few large affiliates making lots of income from Amazon, but I'm guessing these are extremely large, high traffic websites run by big marketing firms. I can't see individuals making a whole lot with Amazon (but I'm sure there's a few exceptions)... The real money is in smaller, more niche specific products and services. For example, I've done extremely well with payday loans (see my sig). Once you pick a popular (and profitable) niche, build a website around that product or group of products. With Amazon, there's just too many options and the commissions are low...
But its also harder to reach people on a small niche. Also it should be a "big" niche. A niche which gets 10000 searches a year isn't very profitable, though you are the only promoter