How can I get songs on my computer if I don't have a disk drive?

I just have a little bitty computer and I can't insert cd's. I have itunes and an ipod shuffle. the only way I can get songs on my itunes is the ones I had on my ipod from my old computer. I transfered those from my ipod to my itunes. I want to put some of my cd's onto my itunes so I can put them on my ipod shuffle. I also have a mac that has a cd insert. Is there a way to put songs from cd's onto my mac, transfer them to my shuffle then onto my itunes? I will be around for a little while if you have any questions.