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The first thing is to have a site with traffic. You should have a site which fills a need or desire, or which offers information on special interests. You probably have a hobby or interest, and know enough about the subject to write something useful to others with the same hobby/interest.

Create a website which makes this info/knowledge available to others. You can then put the ad banners and text links from the merchants on the page(s). (Examples of the banners and text links can be seen in the margins to the left and right.) 

Then, listing it with search engines and following other promotional tactics, get some traffic coming to your site. People who visit your site will have the opportunity to click the banner and generate income for you. 

If the purpose of your site is to sell your own product, make sure you keep your product and your affiliates' ads clearly separate; and don't clutter your page with too many ads. 

Learn how to promote your site in search engines, banner exchanges and link exchanges. (This info is readily available from several sites on the internet; just search for "website promotion")

Keep going down.............

Don't just publish a page of affiliate banners. Besides looking terrible, it shows a lack of experience. Also, some search engines may reject you.

Give your site as many pages as you can. If you can take a reader to many pages you can show more affiliate ads; just remember to make it worth the extra click by giving the visitor something of value on each page. 
In fact, you can probably think of several different themes for websites, and with the many free website opportunities available, you can create quite a few sites. 

Choose the right affiliate. Target your market; if your site/page is about research on ageing, your affiliates should sell wheelchairs not roller-skates.
Also, concentrate on affiliates that offer higher priced items . Don't ignore the lower priced ones, but remember, it takes a lot of traffic to get even one sale, so if that sale is worth more you earn more. 

Build a "Downline".  Most affiliate programmes will pay you for referring others to join them, and give you a subsequent commission on their sales. Find people with websites, especially high traffic sites, and get them to sign up through you. If you can design sites, offer to do it free in exchange for becoming a sub-affiliate. One good sub-affiliate may generate more than your own site does.