Firstly, you need to understand the basic concepts of SEO.. but if your asking this question then I guess you do... check the basics out on their website, age, keyword density, and just general basic onpage optimisation techniques! Secondly and most importantly, you need to be looking what their doing behind the scenes (offpage opt), check their backlinks if they have thousands, dont be alarmed.. only be alarmed if they have thousands from unique IP addresses.. if it seems like all their backlinks are sitewide, and have very little ACTUAL ´points´for their website, and generally seem to lack the basic concept of SEO (an anchor text on link to reach your target) then it´ll be a walk in the park. If your able to send the URL, niche, and keyword here then i´ll be able to help you more.. but if not then you just need to be looking at what there doing, in a backward process of what you´d be doing to get ANY of website #1.
My friend Shadowing competitors backlink is the best way to get top position only when the competitor is at top position on huge number of keywords. I will tell you to only do three major task and rest of the things you will gradual understand. 1) Do the onpage optimization of that site inculding each the source of all the pages. 2) Check each and every backlinks of them and notice the anchor text. 3) Finally find the solution that how you can get backlink from all those websites. Cool mate