Google has a webmasters site where you can see many information about your site. Important metrics are search queries, crawl errors, sitemap information, and keywords. There are many other information you can find there. Just register your site and everything will be available once you visit there. Google will collect all these data automatically.
Another section of important data available on Google WebMaster are Site related error like Crawl error, HTML related error which search engine think is causing seo related issues and site performance.
I want to say something about site performance. I have found that site performance data on WebMaster tool is quite different than what I see from Firebug's net tab, or page speed information. I am using mobile for net connection at my home town and it gives me 100 kbps and even with these connection it is not showing my site that much slow as shown in Webmaster Site performance section. Therefore, I read the help file and found that the data is directly collected from Google Toolbar users with PageRank enabled. So, can I conclude that users from different part of the world who are accessing my website with different network speed are getting my pages as mentioned in site performance section! This is a very vital data which I cannot collect easily but Google is providing free of cost. But it is very slower compared to what I find even on my network connected through mobile device (100 kbps speed). It is disheartening me. There was some truth in my website slowness over time which I have rectified recently.