Usually, if your phone is 'unlocked' then it is simply a case of switching the phone off, taking out the old SIM card and put the new carriers SIM card in and switch back on. As soon as the phone is fully booted up you should see good signal strength and the name of your new carrier (possibly) at the top of the screen. You may get a pop-up asking who your new carrier is and you can just select them from the list and press OK and your on!
However, if it is not truly unlocked then you may need to 'root' the phone, whereby you have total control over the handset's operating system and the like - be warned though, you could end up causing quite a bit of pain if you mess up while in root mode. Just take it easy and seek good advice and you should be ok though - no worries ! It isn't that big of a deal actually, you just need to be careful.