I have my iPhone and iTunes set up on a specific computer but want to transfer this to another computer.
Do I just install iTunes on the new computer and just sync my iPhone etc.. or is there anything special I have to do ?
There are a couple of ways to achieve what you want to do:
If you have an iPod (not iPhone or iPod Touch), you can follow Apple's official method :
Otherwise you might want to read about the various other methods to copy your iTunes library to another computer (may it be a Mac or otherwise):
This is the method I used successfully which does not require any other third party software:
On a related matter, should your iTunes library ever get destroyed (disk failure), stolen (together with your laptop) or simply corrupted; there still hope if all your music is on your iPod or iPhone. Senuti is a (non-free) software that can recover music from an iPod or iPhone when the original iTunes library it was synced from is no longer available for the reasons stated earlier. How to Use Senuti
If your entire library is already synced your Pod, you can use Senuti to copy all the music on the device to the target computer of your choice:
Senuti is available http://www.fadingred.com/senuti/
The trial version can only recover/copy up to 800 songs.
I purchased a new laptop the other day and found the best solution was to install myTuneSync on each computer, then use it to synchronize the two libraries. This avoids any problems with paths, Windows/Mac conversion, etc.
After doing that, you'll need to sync the iPhone with the new computer, which will dissociate it from the original computer.