Of course, those results will be different for each search word or phase for each engine or index and may vary from day to day or even by individual search. Some sites consistently rank pages the same way each time, and others randomize the order within certain groupings.
The first task is to determine which keywords or phrases are likely to be used by potential visitors to your site. This can be broken down into two subtasks: Finding all the keywords and phrases that you think should find your site, and finding the ones that people are already using to find your site. The second is far easier, and a good starting point. You should be able to get the referral information from your tracker.
This tells you which keywords or phrases and which search engines or indexes were used by the recent visitors to your site.
Figuring out your ranking for each keyword or phrase for each search engine quickly adds up to a huge job, even to do once. And you really need to do it regularly since the search engine algorithms are tweaked every once in a while and their indexes' content changes constantly.
Therefore, you really have to use some software to handle this job. Luckily, there is at least one good free program to do this (see the form below), and some excellent ones that are relatively cheap.
Using the software, you can see which sites rank higher than yours and try to figure out why and how to improve your ranking. For example, by further optimizing your meta tags or improving the frequency or position of keyword appearances within your page's content.
One key to good ranking is having many quality sites link to yours. There is a link below to a free service that will provide this information using the major search engines.