Well, the user has to click on an ad and then hit the thank you page. They also have to have cookies enabled.
If you don't want to wait to see if it works, you can lower your bid for one keyword, wait a while, then search for it in Google and click on it. Then if you hit the thank you page you should see a conversion show up in the Adwords account, but it may take some time to show up.
I think you will also see this in the analytics, but I'm not sure where.