There an App in the App store cant remeber what its called but does what you want it to do. Its free as well.
Just fire up itunes that the phone is configured through and tell it to do a backup. Shut it down, take out the sim, put it in the new phone and setup the new phone. Using iTunes follow the onscreen options to get it to restore the settings/programs/music etc to the new phone.
My contacts are stored on an Exchange server though, so some of what I have written might be different for you.
Did you just renew your contract and get another iPhone 4? Am genuinely a bit puzzled by this one The backup and restore is really really easy on iTunes, you'll be fine with it.