There are a few things that you should know when you are looking to analyze your website. First, understand if you have chosen the right keywords for your website. You can use various tools to do that. Google Keyword tools are widely used for keyword research as it is free and gives good results. Check the link for the Google Keyword Tool
Once you have done this then see how your website is being optimized, in the sense if you have all the right ingredients in your site that co-relates with your keyword goal. If you want to save your time you can use seocentro.com to do this research.
If you have completed this step, add Statcounter and Google Analytics into your website and start monitoring the kind of traffic you are getting.
Link for Google Analytics: http://www.google.com/analytics/
Statcounter Link: http://www.statcounter.com
You can also use marketing.grader.com to see the traffic, leads and analytics.
Using Alexa.com is another good way to check your website history and analyze your site. That also gives you good details of your website.
Do not forget to use Google Webmaster tools. Google Webmaster Tools provides you with detailed reports about your pages’ visibility on Google.
After you are done with identifying what is works well for you, the next step is to analyze why it works for you. Then mature to the step of what is not working and then when you know why other things are working you can put the non-working keywords to work.
With all the above steps, you will know how to analyze and implement the on-page factors and simultaneously work on your off-page techniques to secure back links.
If you are using Google Adwords, you can perfectly analyze what kinds of keywords are commonly searched and their cost. You can understand the pattern of search from a consumer’s stand point and implement those things into your SEO campaign.