I moved my in-laws from AOL to Thunderbird (they just aren't ready to use just web mail) and needed a way to get their address book out of AOL. I did some searching and found a couple of possibilities, but nothing easy and free. I'm pretty sure there isn't an option to export from the AOL client, but I found the way to do it.
Use the AOL webmail interface and you can export your address book to an LDIF file. Clean it up if you need to and then import it into Thunderbird. Simple!