A proprietary algorithm, well guarded by Google, though often guessed at.

There are many factors but the major ones (I believe) are number of previous click-thrus and the link’s “page rank” which is an algorithm Google came up with and is determined by the “page rank” of other sites/pages pointing to the search result.

With the use of SEO’s or search engine optimization techniques by the website. Of course, those who pay for ad space will always be on the top of the list before the non-paying websites.

The Top searches in yellow that says “sponsored links” are people who use Google AdWords. This is a paid subscription to have ads that run cyclically and get ranked based on clicks and search terms. The ones you see in the yellow are the top rated, and then the remaining filter to the searches on the right side.

To be higher in the regular searches, using a Optimizing service is what helps. Linking between websites helps, having keywords appear more in your website, even the little things such as coding a picture name to enhance result. There is so much that goes into this arena that it is impossible to explain it all!

Then there’s this answer.

Generally, the amount of traffic that the site receives, and the keyword selection, and how much the webmaster pays the Google people, blend together to determine page rank.

I don’t think so, @Nullo. Google is very proud of and secretive about its page-ranking algorithms, as @dpworkin says. I don’t believe you can buy page rank; that would certainly compromise the algorithm. One thing that does count, though, is how many other sites your page is linked from and what their rank is.

Google.