#2 first: Try the disk in another drive before you blame your drive. Then try cleaning the disk AND the drive (canned air & a laser disk cleaner - available @ Radio Shacks for $5.)
Is the drive brand new? . . .
Now on to #1: Unless you have hardware-specific driver/details available (see end), then the only way is to open up your case, remove the drive, and read its label.... (There IS software out there that can get that info somehow from the drive's ROM, but I don't know of any off-hand. You could Google for them, but if you do, BE SURE to virus scan anything you download!)
To see the info about your CD/DVD drive info:
0) Start -> RIGHT-click My Computer, select "Properties"
1) Select the "Hardware: tab
2) Select the "Device manager" button
3) In the Device Manager window, click the "+"-sign in front of your "DVD/CD-ROM drives" line
4) RIGHT-click your listed Drive device and select "Properties"
5) There probably is NOT a valid name listed in the "Manufacturer:" section, so instead, get the device's ID info, thusly:
Select the "Details" tab, and assure that "Device Instance Id" is selected.
6) Click on the line of jumbled text, and then copy it (via <Ctrl>-C on your keyboard.
If you can't decipher what is hidden in it, post it here, and I'll tell you waht it means. As an example, here's mine for (one of my) DVD drives:
IDE\CDROMHL-DT-ST_DVDRAM_GH20LS10________________FL00____\364B38314C323232333720352020202020202020
The key chunk here is "GH20LS10". A quick Google search and I see that it's an LG GH20LS10 DVD drive!
7) Close out of all opened windows via the "Red X" method....