After you go through the process of setting up a free account with Google Analytics (http://www.google.com/analytics/), follow the steps to add your domain and get the tracking code snippet.
1. From the Analytics home page, click on the link that says "Add Website Profiles";
2. Add your domain URL (address);
3. Click on "Finish"
Google Analytics will provide you with a snippet of code that must be added (via copy & paste) to your site's pages in order to track visits to them.
At this point you have a couple of options:
1. Modify your footer.php file to add the code just above the </body> tag;
2. Install one of several WordPress Plugins that will put the code in the right spot for you - once you install the plugin, follow it's instructions to paste the code, and it will add it to your pages.
A few good WordPress Plugins for handling Google Analytics:
http:
//wordpress.org/extend/plugins/google-analytics-for-wordpress/
http://wordpress.org/extend/plugins/google-analyticator/
http://www.semiologic.com/software/google-analytics/
NOTE: I cannot comment on these plugins beyond the fact that many users seem to like them, because I don't use them - I just pasted the code into my footer.php file. Feel free to try them all to decide which one you like best HOWEVER don't try them at the same time, or you'll triple the Google code and skew your results.