It all starts with a review of their site designs and layouts. Do any of your competitors have Java- or Flash-heavy Web sites? What about the navigation scheme; does it pull you through the purchase funnel--and does there seem to be an overall branded theme? In terms of content volume, how many pages do they have (on average) compared to you? You may find that you're well ahead (or far behind) when it comes to depth of content.
Check the rankings for your desired keywords to see where your competitors turn up, and then compare that to the keywords they seem to be trying to rank for--as they may be different. How keyword-dense are their content pages, and if you can scan the Meta data, are they tagging images, videos and other multimedia effectively?
Lastly, check off page factors like Google PageRank and traffic rankings via Alexa or Compete, and scan (and compare) the number of incoming links they have, as well as the quality of sites they come from. And you should also be aware of whether your competitors are using spammy tactics like cloaking--as it's a sign that they may end up using dirty tricks against you once you start showing up in the rankings.