There are a couple of ways you can transfer your contacts to your new phone:
If you want to transfer your contacts from a non-Three phone or SIM card you'll need to back up your contacts to your computer using the software that came with your old phone.
If you don't have this software, or never got it with your phone, visit the phone manufacturer's website where you should find links for downloading the software you need:
You'll need to enter the serial number in the search box. You'll also need to download the right software for your phone (like PC Studio/PC Sync/Kies).
If you've already got a Three SIM card and just want to transfer your contacts from your old phone to your new phone:
Your contacts will now have been transferred.