I use the fast and free AmiCDFS on my Amigas to read CDs and DVDs. I also use it to read discs from an external CD drive through the Subway in an A1200. You can get it here:
http://aminet.net/package/disk/cdrom/amicdfs240Once installed, you simply configure it to use the Subway device. I'll run through it myself and type up full instructions if you want.
You won't be able to burn discs through the Subway, sorry. The clockport is just too slow, I don't think it would even work through the new faster clockport on the A604, although reading through that will be nicer. You also won't be able to play CDs through your Amiga's Paula audio. You can use a CD player program to tell the CD drive to start playing a CD, but unless you have an external amp and speakers connected to it, you won't hear anything. Plugging some speakers into the headphone port on the front of the drive would work if it has one. I have experimented with it already, the programs that would normally spool the CDDA data through the SCSI bus and translate and play it through Paula won't work with the Subway.