Depending on your Android front end, when you plug the phone into the computer via usb, you should have a "use as drive" or similar option. Choose that and it lets you read your phone as a hard drive. You will have to poke around your phone's folders to find the one that stores music (likely labeled "media"). If you have songs on the phone already, look for them, that's the folder that your phone's media player looks for. Simply drag and drop the mp3s from the computer to there.
Alternately, depending on the media player you use on your computer, it might recognize your phone as another media device it wants to synch with and synch your computer music to the phone. If you synch all your stuff already, you might use that instead of dragging and dropping.
Alternate #2, if you use Amazon Cloud Player or similar, it will also synch everything.