There are a couple of things to consider....
EDIT, just re-read your post... is your surface an RT or Pro?
Option 1) You should be able to access a shared drive on your network, but will have to have permissions set, etc...
Option 2)
For an RT version...
I believe the Surface RT can access a USB DVD drive in the same manner of the Pro (see below), HOWEVER, from what I have read, it can only read data (can't burn a CD/DVD), and it can't playback a DVD directly from disk as it doesn't have the required codecs.
For a Pro version...
If you want to plug it in directly to the Surface, make sure it is a drive that has its own power supply (needs to be plugged in to a wall for power and USB is only used for data....
If you have a docking station for your surface, you can use a drive that uses 2 USB ports (I believe one is used just for power and the other is data and power)...
FWIW, I bought an LG CP40... blu-ray (playback only) + DVD reader/writer... It uses 2 USB cables, so I can only use it when my Surface 2 Pro is in the docking station.