To open one of the common dark and light gray Dell computer cases, there are two buttons that need to be pushed. There is one on the top, and one on the bottom. It makes sense to lay the machine on its side, then press the buttons together and gently pull the sides apart.
If you force it, you can break the plastic, which happened in this picture of a Dell computer case (hence the duct tape):
I’d like to open Dell precision cases
Jocelin