ETA (August 2015): I am now using ShopStyle affiliate links in addition to Amazon affiliate links. I receive a small commission (usually 2-5 cents) each time someone clicks one of these links, regardless of whether or not they make a purchase. You can identify the affiliate links by hovering over them and seeing if the url starts with "api.shopstyle.com". I do really appreciate it when anyone clicks my links, because it allows me to save a little money to pay for some of the products I review. Read on for how affiliate links in general work.
I'm going to start using Amazon affiliate links again, for a little while at least. I am facing a period of (hopefully temporary) unemployment, and even though not much comes from affiliate links, a little is better than nothing. I am hoping to get enough small Amazon gift cards to buy the only fucking wet food that my princess of a cat will deign to eat, which I can't find in any actual stores around here: the glamorous Friskies Tasty Treasures Beef and Liver Dinner with Cheese (there, that's the first affiliate link). I will only be participating in Amazon's affiliate program. I know there are lots of issues with Amazon, but frankly there are a issues with many of the companies that run affiliate programs, and at least this way I can link to a variety of different items. Also, Amazon doesn't care how much I write "fuck," and other affiliate programs do.
I will always include a disclosure line at the top of every post that contains affiliate links (see above). I will also try very hard not to write in a way that requires you to click an affiliate link in order to get basic information. There are few things that annoy me more when reading a blog than when people deliberately withhold information in an effort to force readers to click their links. For example, they might affiliate-link the words "this one" without naming the product. If I ever do that, you have permission to yell at me. (Sometimes in the past I may have linked vague phrases like that to other posts on my own blog, but I will try not to do that either, if I can remember.)
I know that there are people out there who don't like affiliate links, and I understand that perspective. Personally, I find them to be one of the least obnoxious ways to monetize blog content, since there usually isn't a brand or PR person who needs to be placated. If a blogger introduces me to something that I want to buy, I'm happy for them to make that 8% commission or whatever (from Amazon it's more like 4%). If you want to avoid clicking affiliate links here, don't click anything that goes to Amazon, which you can tell when you hover over the link and see the URL. Some of my old posts have Amazon links that are not affiliate links right now, but I'm going to gradually update them. (On other blogs, to avoid affiliate links, mot likely anything that redirects you rather than linking directly to the brand/store page is an affiliate link.)
I also know that a lot of casual blog readers don't really know exactly how affiliate links work, so let me explain. When you click my link, a cookie will be placed on your computer. That cookie expires in a certain amount of time. With Amazon, it's 24 hours. With some other affiliate link programs, it's 30-45 days. So that means that anything you buy from that site before the cookie expires generates a commission for the blogger. If you click through because I linked to some lipstick on Amazon and don't buy it, but later that day decide to order a DVD of Xanadu, I will get a small commission. If you put the lipstick in your shopping cart during the 24 hour period, wait three days to think it over, and then buy it, I do get a commission for the lipstick, but not for anything you added to your cart after the 24 hours ended.
Similarly, if you were to click on an affiliate link to J. Crew from a blogger using RewardStyle (rstyle), the cookie would be stored for 30 days, and anything you bought from J. Crew in the next month would generate a commission for that blogger. It doesn't have to be the item they linked, just anything from the store. If you want to avoid giving someone commission, you need to shop in an incognito browser window, clear your cookies, or click on someone else's affiliate link and replace the previous cookie with the latest one.
Hope that is clear. Let me know if you have any questions!