Surveillance cameras truly come in all shapes and sizes. Some are as small as the tip of a pen and others are the size of a small sofa. Surveillance cameras used in business are often hard wired to receive electricity while many for use in homes and small businesses are wireless an contain a battery. It's important to know what type of camera you're dealing with and how power is supplied to the unit. A cursory inspection of the camera will give you enough clues to figure out the power source and how to disable it.
Inspect the camera close-up. This will give you an idea if the camera is hard-wired or wireless. A wireless camera will usually be portable and contain a battery while wired camera will obviously show signs they are connected to the structure for power.
Remove the battery or power source. If you suspect the unit is wireless, try to locate a battery compartment for removal. If the unit is wired, the power lines running to the camera will have to be severed.
Disable the camera using a laser. If a power source cannot be determined and you don't want to destroy the camera, a laser pointer is your best bet. These devices are cheap and can temporarily disable the optics within surveillance cameras.
Disabling security cameras for reasons other than maintenance or with legal authority is most likely against the law.