How to put music from iTunes on to your iPhone 4S?

When I first got my iPhone 4S I started it on another laptop, that one broke and now I have a new one. When I go to 'sync music' on this laptop it says Remove and Sync? I don't want to delete anything on my iPhone now, all i want to do is add a few songs?

Added (1). It won't let me drag to the iPhone

Just go to the new songs and drag each of them onto the iphone

Be sure iTunes is set to "back-up before your iPhone to this computer" before you sync it. After it backs up and syncs you can add your new songs.

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