Just restating what everyone said... Google Analytics. Put the code in place then go read a book like Avinash Kaushik's Web Analytics 2.0. Analytics is the hinge that swings the door.
You can use Google analytic and Google webmaster tool to analysis your website. these tools are free to use.......
use Google analytics to track your visitors report and also use alexa report to analyze for top keywords to your website. Create unique meat tags, alt tags, XML sitemap & HTML site map. Check for any broken links and use internal link structure.
Start from basic onwards, like : Page Rank, Alexa Rank, Index Pages, Back Links, Domain Age, Link Popularity, Competitor Analysis, Keyword Analysis, Content Optimization, Meta Data, Technical Problems, design issues, webmaster errors etc..
You can check if your keywords are in the title, the meta description, and the meta keywords as well as spread about naturally in the body, that's a first step
Analyzing links manually is possible but it is not recommended. It is a tough and time consuming work. A much better approach is to use dedicated SEO tools. Such tool can automatically find all backlinks (by using Yahoo Site Explorer) and analyze them for anchor text and PageRank. If you have this information about backlinks you can easily spot additional link opportunities. Another trick is to analyze backlinks of competing pages. Find out where they have placed links and try to place also your links there.
There are seo companies that will do a free analysis in return for future business potential, also look into software that will help you do analysis of your site google..................... seo top software 2011
W3 Validation for CSS, XHTML and Broken link validation and google analytics and keyword tool for keyword analysis.
Google tools are good for analysing the website. Use google webmaster tools also google analytics can tell you how much traffic you have to your website and what type of keywords they are using to get there and a whole lot more.