Wow, how non-specific can you be?
No model names, no model numbers?
How about this non-specific answer: "Carefully!"
The majority of cases out there are 2-piece (with some minor bit pieces for switch covers and the like, but still basically 2 pieces).
One piece for the holding of the motherboard and power supply, and the second piece for innards access.
But, seriously, if it is the type of Dell case I am familiar with, the Dimension style case, the access cover slides back and then off. You first have to remove the keeper screw along the back side and then press in the top and bottom "ears" at the corners, then apply pressure to the case cover and slide it back an inch and then lift it off.
Probably your case is not like that.
And the one TRUE ANSWER would be for you to look at your now broken case, and look at the the method of how it was assembled and held together. Then learn from that. You have the case in front of you, don't you? You should be able to tell us how to open it.
Old Dell case is in two pieces. Got it open but broke off every plastic tab that slips into steel frame under case. At least I think I got them all. Can anyone describe the easy way to remove this two piece case for the next time I go dumpster diving?