Google provides a nice set of free Webmasters tools to help you understand how your website is being searched by Google and how you can make it more "Google-friendly". Google Webmaster Tools are a set of functions and tools that enable you to monitor how well your site is being indexed by Google and how people are using Google to find you. It's a nice set of tools if you want to pay particular attention to optimizing your search results in Google. But it also gives you some idea of how other search engines might be indexing your site.
First, you need to have a Google account before you can set up the Webmaster tools. You also have to be an owner or at least an administrator of the site you want to monitor. For the Webmaster tools to work, you need to "verify" your site with Google. This means placing an html file on your site that has a specific name or by adding a metatag to your home page. Once this is done, your site will be verify and you can start using the webmaster tools.
Note that you can verify and monitor more than one website. When you start the Webmaster Tools, you will see a dashboard that lists all the sites you want to monitor along with their verification status. You cannot remove this verification metatag or html page - if you do Google will no longer be able to provide you information on your site.
Diagnostics
* Web Crawl
* Mobile Crawl
* Content Analysis
The Diagnostics section shows you any problems Google had when it was crawling your site. The Web Crawl shows errors crawling the web site, the Mobile Crawl shows errors on pages specifically for mobile browsers - like cellphone browsers.
Content Analysis is an interesting section. The analysis is based on Google crawl rules. It will tell you if Google sees any potential problems or issues with Title tags, metatags, content that is not indexable (like videos or images). While issues displayed in the Content Analysis won't affect Google crawling your site, they are things you should look at closely as they can affect your ranking with Google (and potentially other sites).
Take a look at Google's Webmaster Guidelines to improve your site for SEO.
Statistics
* Top Search Queries
* What Googlebot Sees
* Crawl Stats
* Index Stats
* Subscriber Stats
Statistics are the really interesting part of th webmaster tools. You can see what people are entering for queries that return your website. Compare this information to other search engines. Do you get the same results? Along with the top entered queries, you'll also see how many people actually clicked the link to your website. All this information helps you improve your metatags, titles, keywords, and key phrases within your site.
The crawl and index stats tell you when you site was crawled and what, if any, problems might have occurred during the crawl. Things like broken links are common problems displayed.
Finally, subscriber stats tell you how many people have subscribed to any feed you have created for your site - at least those who use Google tools like the Google Reader, Okrut, etc.
Links
* Pages With External Links
* Pages with Internal Links
* SiteLinks
This section is also good as it shows you what pages on your site other sites are linking to and what pages link to other internal pages. This helps Google determine how important certain pages are on your site.
Sitemaps
You don't have to, but considering adding a sitemap of your site to Google. It does help Google determine how to best crawl and index your site. Google will then let you know how those links are doing.
Tools
* Analyze Robots.txt
* Manage Site Verification
* Set Crawl Rate
* Set Geographic Target
* Set Preferred Domain
* Enable enhanced image search
* Remove URLs
Lastly, Google provides a number of additional tools you can use to help improve your search rankings.
Manage Site Verification enables you to see how many people are verified to view information about your site. You can have more than one Google Account verified to view information about your website. Google recommends you do this instead of creating a generic google account that everyone has access to.
Other tools include viewing the details of the robots.txt file you may have on your site, setting how often you want Google to crawl your site, set preferred domain if you have more than one for your site, and indicate sections or pages of your site that you don't want crawled.
Final Thoughts
Google is probably the most popular search engine used today. So it definitely makes sense to take advantages of these free Webmaster Tools to monitor how Google is indexing your site and how users are searching for you. That doesn't mean you should ignore how other search engines are working for you.
Take advantage of the information Google is providing you and see if you get similar results with other search engines. For instance, if Google lists a top search term for you, try this term in other search engines and see how it does.
Also, Google Analytics is another free tool that you should add to your analytic toolkit. It's a full web analytics program that can tell you a lot of good information about your website, including traffic patterns.
Together these two tools go a long way in helping you optimize your website for your visitors - which is the key to being popular with Google and other search engines.