how to analysis web site?

[Peter]

I use few tools for this.

First i use SEOSpyder http://www.mobiliodevelopment.com/seospyder/ and do on-page SEO investigation of site. I check all pages, media and links for errors, their links (anchor, alt, etc) , dofollow, nofollow, presense of meta tags, title, H1, H2, H3. There i can see social signals for pages - number of tweets, facebook likes and number of G+es. The most important is to see is everything correct and follow requirements.

Then i use sites as OpenSiteExplorer, AHREFS, MajesticSEO to see what are most popular pages and their backlinks. There i can see what is link juice, anchor texts, distribution of C class subnets, what is backlinks value and much more. I also can use tool as SEMRush to get keywords that this site is being ranked.

Using this is know almost everything for site:
- their internal link structure
- their social signals plus Google PR, Alexa ranking and Moz ranks
- their backlinks and it's value
- site outgoing links and their value
- keywords that site is ranked

I think that this is everything that you can see if site isn't your.