First, I had to sign up for a free Google Analytics account. When it asked for the URL of my site, I put in the URL to this blog (http://agileice.blogspot.com) and gave the new account a name. After putting in my contact information and agreeing to the terms of service, Google gave me some tracking code that I needed to add to my blog site.
To add that code to my blog, I logged into my blog and clicked the "Customize" link at the top of the page. From the "Layout" tag, I clicked the "Edit HTML" link which brings up the actual HTML template for the blog page. I scrolled down to the bottom of the HTML, and inserted the code from the Analytics page right above the closing </body> tag. That's really all there was to it. NOTE: the code *has* to go at the bottom of your page.
Once the code was installed, I logged in to my Google Analytics account. In the stats table for my blog, the cell at the far right was a different color and said "Tracking Unknown": Google Analytics hadn't yet communicated with the site. I clicked the "Check Status" link and the cell changed to read "Tracking Installed". That's pretty much all there is to it.
Now I can easily check the visitor statistics for my blog just by logging in to my Google Analytics account. I can get reports on how many visitors I've had, where they're from, how many hits I've gotten over time, and all sorts of other data views. There are even tools that I can install on the blog that will show the stats updated hourly (though I think I'd rather just keep it on the Analytics site).