How do I add a second site to my Google Analytics account?

You're in luck! Google Analytics is capable of tracking a lot of sites and handling a lot of traffic (as I know from experience). If you're not familiar with Google Analytics, well, I'll just say it's a splendid - free! - tool that lets you get a much better understanding of your site and how it works. You can learn more here: Google Analytics Help.

Now, in terms of your specific question, once you're logged in you'll see this:

As you can see, I have two domains set up, one of which hasn't yet started reporting data to Google (since I just set it up a few minutes ago!) and one of which - this site - has been happily reporting data to Google for many months.

To add a new domain, click on Add Website Profile:

Pretty much, all you need to do here is enter the domain name of your site. Since I'm hooking up my intuitive.com domain, I'll specify that here and click Continue:

Hold on, though. That's not what you want because if you're starting from scratch, you don't want legacy code, so instead click on New Tracking Code and that code is what you want to use.

Now just copy and paste those few lines of text onto the very bottom of the pages you want to track (you'll also need to include the site home page). If you have a blog, congrats, you can add it to the template and just rebuild and have the code added to dozens, hundreds or even thousands of pages automatically.

That's all there is to it. Give it a few hours and you should hopefully be able to log back in and see at least some traffic. Then you can focus on building traffic. :-)