To check and see if the domain name you want to register is available, make use of a WhoIs lookup, which checks on domain registration information. There is a separate post listed various different lookups, but for simplicity's sake you can use the official HostMySite.com lookup found here:

http://hostmysite.com/whois/

One thing to note: no matter which lookup you use, it is NOT done in real time - there's about a 24 hour delay. That is to say, just because a domain shows as available through a WhoIs lookup doesn't mean that it actually is. The only way to find that out is to actually attempt to register the domain name - we'll recieve an error when doing so if the domain is already taken.