I am seeing this question a lot in ppcclassroom.com so I thought I would post this information.
For the Google Search network, how you rank on a page is determined by your Adrank. You can refer to Google for the answer here ( http://adwords.google.com/support/bin/answer.py?hlrm=en&answer=6111 )
But briefly Adrank is a number that is determined by your minimum bid times your quality score.
Google mentions that The Quality Score for Ad Rank on the search network is determined by:
* The historical clickthrough rate (CTR) of the ad and of the matched keyword on Google; CTR on the Google Network is not considered
* The relevance of the keyword and ad to the search query
* Your account history, which is measured by the CTR of all the ads and keywords in your account
* Other relevance factors
Aside from keeping your ad relevant to your keyword and keeping your page relevant to your ad, you need time and clicks to establish a good CTR for your ad.
If you are competing for someone against the same display URL then you will need to bid more initially until you establish account history. Also *very important* start split testing 2 ads against each other right away so you can establish work on a good CTR right away so that with a good CTR and ad history you can start dropping your bids.
I believe Adrank is new as of 2007 – before your position was determined by your bid times your CTR ( Click Thru Rate).
Regardless the Google Quality score is here to stay as they focus more on the user experience. So remember to start split testing ads against each other right away and keep your ads relevant to your keywords and landing pages.