This is a very, very general question. The best way is to match the strength of the top ranked competitors. Sometimes, it can be very frustrating as you might see a site with few back links never giving up the number 1 spot.
That would probably be because the domain has a lot of trust rank in the eyes of Google.
Look at this example. There are so many people competing for the acai berry keyword. If a big medical website like webmd.com or ehealth.com were to create a supplemental page on acai berry and do some basic SEO like back links etc, they are just going to jump to number 1 beating all the webmasters who have thousands of back links.
But, in most cases, sites like these do not do it for commercial reasons and will just write an article and leave it as it is. Sending just one or two back links to pages like that can push it up to the top 3. This usually happens naturally when someone links to sites like these on their blog. That is true and natural back linking that will probably never happen with your affiliate site.
You just have to work in niches where big player authority sites do not have a big presence. If they are there, it is not impossible to beat them, but it is also very difficult at the same time.