Let's say I want to host DOMAIN.COM on one server, and FORUMS.DOMAIN.COM on another server. How would I go about doing this?
It all depends on a lot of factors, the main question is Who is hosting the DNS for the domain? Generally you can email your hosting company and say: Hey, hosting dudes can you add an A record for me, I need forums.mydomain.com to point to this IP address xxx.xxx.xxx.xxx"
Yes, that can be done by editing the DNS zone records for the particular domain (zone files are easy to mess up, be alert!)