After setting up the domain controller for my environment, I turned to the database server.
This server is another virtual machine running Windows Server 2008 Standard. Once the server was created I tried to quickly add it to my new domain. Immediately I had an issue because I kept getting an error that said the database server couldn't find the DNS server (however I was able to ping the domain controller from the database server and vice versa). I ended up calling my brother (nice to have a network admin in the family) and he helped me configure the DNS for my domain controller. We found that my domain controller didn't have the correct settings for the DNS forwarding servers (he said they needed to be set for Verizon's DNS servers). I also had to configure the database server so that its DNS server was the domain controller.
Once we got through those issues I was able to add the database server to the domain. After that I installed Sql Server 2005 on the database server (following the directions in the guide) and made sure I could run queries against it.
Note: At first, when I tried to activate Windows I got an error that said there was a DNS problem. I went to MSDN and retrieved a new product key. After that Windows Server activated without a problem.