I have a new MacBook that doesn’t have a CD drive.
I’ve got several old CDs that I want to burn to iTunes so I can get rid of the physical CDs.
How do I do that? 
“Burn”? To iTunes? Is that what they are calling it nowadays? Don’t you mean converting from a CD WAV file to something more universally playable like MP3? If so, get an external CD drive connected by USB and use a CD ripper program.
If you want to get music from a CD to iTunes, you want to “rip” the songs from the CD. (“Burning” songs means to go the other direction, i.e. to record songs onto a CD.)
Anyway, you need to buy an external optical drive, something like the Apple USB SuperDrive.
Or, since he only needs it temporarily, he could possibly borrow one.
Worse comes to worse, he could also get a regular CD player, plug it up to the line in jack, and record it to a file. But I would not recommend that unless you absolutely had to. It will take a lot longer, you’ll have to manually separate each of the songs, and the quality will be lower–even if you record as well as possible and normalize the files.
I’d see if I could use another computer with a CD drive and then save the resulting files on a USB stick before I’d go the CD player route.
Or for less than half the price he could get a standard external optical drive, with the advantage that it complies to industry standards and will work with any system, unlike the Apple one that doesn’t even work with all Apples.
Given you own the original source media, there is a case to be made you can morally (perhaps even legally) torrent the music.
Yeah, as the owner of many an Apple, just find a cheapie external optical drive on Amazon with reasonable reviews. I can’t remember what I paid for mine, but it couldn’t have been more than $30 for an optical reader/writer (CD and DVD.)
I bought an external USB drive for about $25 on Amazon. It’s lasted over 2 years so far.