How do i listen to and add music to an ipod that has been synced on another computer?

My mom got and ipod shuffle from a friend for her birth day and her friend had put songs on it and when I went and put it on our computer to see what kind and how many songs were on there. I also was going to add some songs that were on our itunes from when i put songs on my ipod. when I pluged it in and opened itunes it didn't show up on the side colunm and a message popped and said that i was not authorized to play some of the songs on the ipod but when i went through the authorization process it didn't work what can i do