Unfair Apple Limitations
One of the worst and most surprising problems that people encounter with the iPod, iPhone, and iPod Touch is that when you plug into another iTunes account you do not have free range to download that music. It seems like a perfect set up, where you would be able to take around your portable storage device for media and capture up all the music you want from your friends. Unfortunately, Apple has tried to protect the music industry and their own iTunes interest and have allowed you to properly sync only to one iTunes account. That does not mean you can’t take some music from somewhere else. There is a very quick and easy way to take the music you want from the computer you want whenever you want.
The first thing you need to do is find the first song you are going with. It is probably going to be easier to organize if you go for full albums, but the iPod generation has ruled in favor of selection rather than inclusion. Right click it and select to "start a new playlist" with this song. Once this happens the playlist will then appear in the playlist section on the far left side of you iTunes. Name it something identifiable. Now begin going through all of the songs that you want, adding each of them to the playlist individually.
Once you have put together a complete playlist of songs you want from that computer go ahead and plug in your iPhone. Make sure that you select NOT to sync the device to this computer otherwise you may lose everything you have on your iPhone. Select the iPhone in the device list and then go to the Music tab. Here you will see a sync menu with a box at the very top reading Sync Music. Check this box and then hit Yes on the window that asks you if you are sure. Then click on the box labeled Selected Playlists. Go down and find your playlist and select it. If you do not want to get the music videos on this account make sure to check out the box listed Music Videos.
This does not work on every iTunes set up, but it will on most. Go down to the bottom of the screen and select Apply once you have checked all the boxes and see if it will work for you.