Disconnect the cabinet from the amplifier. You cannot have any power running through the cabinet when you test it. A guitar cabinet does not have its own power outlet, so it receives power from the amplifier. Disconnecting the amplifier chord from the input jack on the cabinet will prevent any power from going through the circuitry.
Remove the back of the guitar cabinet. Most cabinets have screws that can be removed with a screwdriver. Set the back aside. If the input jack runs through the back of the cabinet, take the back off carefully so you won't pull any wires loose. Set the back aside, but keep it close enough to the cabinet to prevent pulling the attached wires loose.
Identify a wire you would like to test. You should choose a wire that is easy to disconnect and reconnect. Disconnect the wire. You cannot test the resistance of a wire when it is connected to a circuit.
Attach a digital ohmmeter to the wire. The ohmmeter will have a black lead and a red lead with clips on the ends. Attach these to each end of the cabinet wire you removed. Turn on the ohmmeter, and it will give you a resistance rating. Repeat the procedure to make sure the reading is accurate.
Reattach the wire where it belongs in the speaker cabinet. Replace the back of the cabinet. Use a marker to write a note on the back of the cabinet. Example: "4 ohms." This will remind you of how your cabinet is rated, in the event you get a new amplifier that is ohm-rated. If the amplifier and cabinet have the same rating, the full power of the amplifier will be used.