How do I transfer my iPhone and iTunes application to another computer?

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 :

iPod 101: Backing Up Your Library

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):

How to Transfer iTunes Library to Another Computer

This is the method I used successfully which does not require any other third party software:

How to Transfer Your iTunes Library to a New Computer in Five Minutes

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 - Copy music from iPod to Mac

Senuti is available http://www.fadingred.com/senuti/

The trial version can only recover/copy up to 800 songs.

You can using iTools it has many funtion to backup and copy data from Iphone, access to many folder in iphone and with visually interface, it's very easy to use.