Removing a DVD drive is usually straightforward. It will depend on the manufacturer, but the standard method is to flip your laptop over (placing it on a towel to avoid scratches) and remove the screw towards the middle of the laptop. This will typically be indicated by a small DVD icon.
Some laptops will have a push-button removal system; alternatively, there might be a catch to depress while the drive is removed. This is similar to how you might remove a laptop battery.
You’ll need to slide your fingernails or perhaps a credit card into the gap between your DVD drive and the computer in order to start sliding it out. There should be no resistance, however.
Once the drive has been removed, use a screwdriver or plastic knife to gently remove the fascia.