Most computers come in either tower-sized models or desktop-sized models. Tower cases usually have screws that secure removable panels on either side of the case but will sometimes feature release buttons instead of screws. Desktop cases usually feature easy release buttons that allow you to open the case but some will feature screws similar to tower cases.
For detailed steps on opening your computer's case, see How To Open a Standard Screw Secured Computer Case. For screwless cases, look for buttons or levers on the sides or rear of the computer that are used to release the case. If you're still having difficulties, please reference your computer or case manual to determine how to open the case.
Note: These steps show how to reseat any standard PCI expansion card like a network interface card, modem, sound card, etc. However, these instructions should also apply, in general, to other types of cards like most AGP or PCIe expansion cards and older ISA expansion cards.