What is the best way for an affiliate to sell a product without using Google AdWords or e-mail marketing?
Different types of marketing work best for different types of product leads. In other words, what works well to promote one vertical in affiliate marketing may not work well in others.
Also, it depends on whether you are looking to make a quick hit or intent on building a sustainable business.
There are lots of ways to approach product sales as an affiliate. You could run a coupon/rebate site, reward/loyalty site, comparison shopping site, content site, data feed site, etc.
You could also move into the realm of Web 2.0 and do some things with blogs, RSS, social networks, wikis, video, podcasts,etc.
Personally, I would encourage you to sit down, write a business plan, and work on a site with a long term vision. Come up with a unique value proposition and test out all sorts of methods with different affiliate programs to determine what works best for you.