Laptops not my speciality, but I briefly played with an ancient 315 Satellite a while back...
Because your model will be a lot younger than the 315, the following is only likely to be a generalisation:-
Remove battery, remove any PCMCIA cards etc., remove screws in base, and possibly also on the back of the machine. A small plastic section of casing between keyboard and screen needs to be flexed to remove (it's snapped in place). Lift out keyboard and carefully disconnect flexible ribbon cable. The main plastic case surround is also snapped into place and needs to be carefully eased out bit by bit - I used a small screwdriver to do this. As I recall, in the 315 this casing also supported the two loudspeakers and the screen, all of which need to be carefully disconnected before removal. You should now be able to see the screw fixings for the DVD drive.
Good luck!
ROGER - G0AOZ.