how do I transfer music from my iphone to a new computer?

You don't. its a one way sync itunes to iphone.

Unless the music was purchased in the iTunes Music Store. If that is the case then all you need to do is visit hte iTunes Store and click 'purchases' on teh sidebar and download the songs you want. But like razmee209 said... If these were not purchased from iTunes you would need to find that media and copy it over; music cannot be copied from the iPhone.

What should be done, is to copy your entire iTunes folder from

your old computer to your new one, then open iTunes holding down

the shift key. You will get prompted to create new or open existing,

select existing and navigate to the iTunes folder and select the

"iTunes Library.itl" file.

To find were the iTunes folder is:

http://support.apple.com/kb/HT1391

After doing this, you "should" be able to sync normally.

If you never previously synced to iTunes, then it could be problematic.