This might sound odd, but I think one of the best ways to rank above your competition is to somehow get backlinks from them.
One way is if they allow commenting, with your site/page URL. Deep links from your competitor is awesome.
What I do is find SERPs in which I rank for various keywords and then go to my competition's page and, if possible, try to get a backlink to my corresponding page. The key is to leave a good, thoughtful comment so your comment doesn't get blocked/deleted.
You might even be able to ask them to link to your site. They may not realize that a page of theirs is competing with a page of yours.
Any other tips?