Removing an oven door can sometimes seem like an impossible feat, I will talk about several different oven door removal process.
First and most common is by placing the oven door in the broil position, once in position you simply lift and slide the door off. The door may not want to come at first, by lifting on one end at a time try to lift the door evenly, this will prevent the door and hinge from binding.
Another very common style hinge has a locking mechanism, it ensures the door will not be lifted or pulled off the oven itself.
Using a small screwdriver simply pry the lock down and out of position, if you are unsure of where the hinge lock is, they are situated at the end of the hinge where it enters the cavity. The screwdriver will allow you to retrieve the metal tab out of the cavity and in the unlock position, once in unlock position lift the oven door up as if you were shutting it and pull out.
Once out you will see how the end of the hinge connects to the hinge mount. If replacing the hinges you may have to put them back into the lock position to remove the hinge from the door casing.
On some older Kitchen Aid ovens the door needs to be in the broil position, and you will need to pull straight out on the bottom to remove the door, took me a minute to figure this one out a few weeks ago.
Removing the door will allow you to get to that dirty door glass, take extra per-cation when removing the glass, also assembly the glass in the same way it when in. The middle glass has a special treatment on it to reflect the heat back in, this helps keep the outer pain of glass cooler since there are oven glass temperature restrictions.