There are several levels of research on your competitors that you can do effectively on your own. The first level of research is simply getting a pen and some paper and “crawling” the site yourself while making notes on structure, anchor text, and navigation. This is a way to get fresh ideas about your own site’s navigation, anchor text, and structure.
If you want to dig a little deeper, look at the html source for a competitor’s page. Usually ctrl+u will get you this information, or it will be under the “Tools” menu. Look for well-made title tags, H1, H2, and H3 headers, and a regular smattering of nofollow tags. These are signs that they know their SEO.
You can download a free back link analyzer like the one from SEObook. Using this, you can analyze, say, the top hundred back links by PageRank and Alexa Rank. All you have to do is load them into a spreadsheet and order them that way. This lets you see where their best links are from. If there are bunches of back links from one domain, the competitor probably owns that domain. Figure out where your best bets are for finding your own back links, and start asking. You’ll probably get at least a few good back links this way.