I searched Google search APIs and didn't find a way to get a website position rank based on a searched keyword and i thought its impossible.
But i found by luck this website "http://www.tools4google.com/search-google-position/keyword_tracking.php" which is doing the same as i want to do, so i just want to know the idea behind that, or its something illegal.
I imagine it searches for the keyphrase and then ticks down the list until it hits your domain. Pretty intense but very simple through the API.
It most likely is just scraping the results from all the pages Google gives you. That's why the maximum "number of positions" it lets you select is 1000.. because that's the maximum number Google will typically show you when you do a search in Google. Another thing that gives it away is that the time estimates they give on the page seems to grow linearly... if they used any sort of API provided by Google (or otherwise) it would ideally provide an indexed lookup based on the keywords.
What I mean by scraping is it uses a bot that goes through EVERY page result in Google (for a particular keyword*) .