Unfortunately, selfie sticks are manufactured with very different designs one from another and with very wide range of standards (i.e. you can get worthless garbage or overbuilt luxury), so it is highly difficult to know all possible connection/activation mechanisms.
Use with smartphones
A huge number of s. sticks are made for smartphones, meaning that most of them wont have a tripod-like mount, but some sort of adapter to fit a phone directly. Since a lot of phones with a camera also have bluetooth capability, there are some sticks that have a bluetooth shutter button that you should "connect" with your phone and you shuld be ready.
Some phones (at least the iPhone) can use the button on the headphones as a shutter, so, some sticks have a button wired with a headphone plug.
There are also bluetooth shutters sold independently (not as part of a stick). You could glue, velcro or tape one of these if you can only find a stick that doesn't have an integrated shutter.
Using with cameras
There are some sticks that do have a tripod like mount and almost any camera, even point and shoot, have a tripod screw receptacle.
If you are lucky, you may find a stick like these that also includes the phone to tripod adapter. Such adapters or mounts are also available by separate.
However, not every camera has the remote shutter function. Some may have a remote shutter port, but this is usually the case only with bigger DSLRs that are unpractical to use on a stick. Some compact cameras may have this port though.
Other cameras may have an infra red sensor to accept a remote control. This remote control can usually be bought from the manufacturer but some "generic" controls may work with some cameras. (I doubt a stick with i.r. shutter is to be found, so, if this where the only option for my camera, I'd tape or velcro the remote control to the stick).
Some cameras may have the functionality to be remotely controlled via wifi, bluetooth or other, and in some cases that means a smart phone app exists for that. However, controlling a camera stick with one hand and a smart phone on the other may prove unpractical, I'd just use the phone directly.
In any case, you should refer to your camera's user manual. If the camera has some remote shutter function, the manual should have at least one short section describing it. You can also look at the "optional accessories" list. If there is a remote shutter, then you camera is likely to have the function.
Finally, there are some sticks that have a mechanical remote shutter, that is, a mechanical contraption where a remote lever, brace, clamp, whatever... presses the actual camera's shutter button. This option may have limited compatibility due to the different camera designs and sizes.
If there is no remote shutter for your camera, or you don't want to pay the outrageous price they may ask for it, then you are left with one last option: the timer shutter release. Many cameras have a function to delay the actual shooting for anything from 2-15 seconds. That should be enough to press the button on the camera and re-position the stick.