How to transfer iTunes library from iPhone to new computer?

I got a new computer as a graduation present, and I want to know how I can transfer my iTunes library from my iPhone onto iTunes to the computer. I can't re-download them onto it, seeing as I didn't buy the songs. 5 stars goes to the person who gives the easiest successful strategy.

Added (1). I no longer have the old computer so I can't do the sharing feature

Make an iTunes account
Activate home sharing on original
Download iTunes on new
activate home sharing on new
drag files from home sharing to libraries

Using iPhone transfer platinum. See detail info here:
http://www.video-dvd-ripper.com/#iPhone Transfer

I use one from here: http://www.bestsoft4u.com/article/top-three-iphone-transfer-reviews.html

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