Here's what I ended up doing: Once you log into the domain you registered with Google Apps (by going to https://www.google.com/a/[domain name here]), you can go to the "Domain Settings" then the "Domain Names" section. Once you're there, you can get to the actual domain registrar's site (Google partners with a couple other companies to register the domain name; it doesn't register the name itself) by clicking the "Advanced DNS Settings" link. In my case, I registered the address with eNom, who has a fairly straightforward interface for managing the various parts of the DNS entries. In my case, I needed to edit the "Host Records" section where wanted to forward the "www" host to my actual IP address.
In the "Host Records" section, there are actually a few types of entries; the two types that really mattered in this case are "A" and "CNAME". An "A" entry stands for an actual IP address; a "CNAME" entry is more of an alias, forwarding the host to the "named" address in the entry. When I registered with Google Apps, eNom automatically filled in a number of entries for me, setting a few "A" entries to what I assume are Google's IP addresses, and then aliasing a number of other services (Mail, Calendar, etc) to the Google services address "ghs.google.com". All I ended up doing was changing the "www" entry (which Google had set as a "CNAME" entry) to an "A" entry pointing at the static IP address I have through my ISP.
It took a little while for the changes to propagate through the net, but now when someone goes to www.agileice.com, they'll actually get the pages I'm hosting here rather than being forwarded to the Google pages (or they will once I actually start hosting some pages here ;)). And things like Google Mail for agileice.com still work.