Some cameras can't do multiple exposure, even with trickery. In that case try and borrow the use of somebody's camera that will do it. The author of the photograph is the person who supervises the taking, not the owner of the camera. If you line the shot up and request the owner to take the photo, it's your photo.
To find out how to do multiple exposure you will have to consult the manual for your camera. If it doesn't state multiple exposure specifically then all is not lost, as the following method can sometimes be applied. Old manual wind and rewind cameras can do it by slightly tensioning the film rewind lever then holding in the film rewind clutch button, usually on the base of the camera, and then operate the thumb lever to reset the shutter. This will cause the film to not move on so that the next exposure taken will superimpose on the previous one. This method can not be guaranteed to hold the film perfectly still, and some mis-registration may occur.
Some later manual cameras have a small lever or button right near the thumb lever that will cause the shutter to reset but stop the film moving when the thumb lever is moved. This method is also not guaranteed to provide perfect registration but the few tries I've done with that sort of mechanism have worked just fine.
The easiest to use are modern all electronic cameras where the number of multiple exposures can often be dialled in, usually from 2 to 9. At any time during the multiple exposure the number can be dialled back to one so that the next exposure will be the last and cause the film to move on. Or at any time during the multiple exposure the count can be increased so that the final total will be any number you choose. The film will finally move forward when the last exposure is taken. This system usually provides perfect registration. Unfortunately the marketing department of most camera companies seem to have decided that multiple exposure is a feature like depth-of-field preview that only professionals and advanced amateurs will need, consequently the multiple exposure feature is rarely found on low and mid range electronic cameras.
Exposure has to be modified or not modified depending on the method of multiple exposure used. Some experimentation may have to be done to get the best results. It is quicker to do all the experimentation on the one film and take notes on what you did. This way you will know for future efforts what to do, and as a bonus, in amongst the shots may be one that works out just fine.
It is best to use a colour negative film and cheap processing for these experimental efforts as this film is very forgiving of exposure errors, especially over-exposure. Don't just look at prints to "see how they came out". Always look at the negatives to see how the exposure was. A "thin" negative is under-exposure, and a "thick and muddy" negative is over-exposure. Ask an experienced club member to look at them if in doubt. When you have exposure worked out, then try your usual film and processing or slide film if that is your normal medium.
So far I have listed twelve different ideas to try with multiple exposure. This list will expand and modify as I get feedback from you.
It is essential to use a tripod and remote or self timer shutter release. If your tripod is not a sturdy model, then use it with the legs set at their shortest and don't extend the centre column. You may have to find something stable to place this new short tripod on, like a sturdy picnic table or a convenient wide topped wall.
If you take your eye away from the eyepiece when taking a shot, block the light from getting back into the eyepiece as the exposure may not be correct. Use a bit of black cloth or the eyepiece cover that is supplied with the camera.
1. Multiple images of one person or subject against a dark background. Keep the camera pointed in the same direction and have the subject move to pre-determined spots so that there will be no overlap of the images of the subject. Use flash at night with no close background or foreground appearing in the picture. Any foreground will be overexposed, and any overlap of the subject images will be overexposed.
2. Cut out complementary shaped masks and hold them in perfect registration in front of the lens, maybe using a Cokin style filter holder. Take a scene with the centre only masked then swap the centre mask for the outer mask and for the second exposure take the subject you want in the centre. Typical shot is to have the happy bride and groom fitted into a champagne glass. It will probably take a few tries to get this method to work. You may have to set up coloured backdrops to make sure the merge of the two exposures looks smooth.
3. Multiple shots, each taken with a different strong coloured filter, the exposure for each shot should take into account the filter factor. Through the lens metering makes this one easier. Use this method on moving objects like people walking along a street, traffic going by or waves breaking at the sea side. Results can vary from boring to bizarre to interesting.
4. Big moon shots. For the first exposure use maybe a 35mm lens and take a time exposure night shot of scenery leaving a fairly large area of dark sky available. Then move the camera, fit a telephoto lens (the longer the better) and take the second shot of the full moon so that it will end up in the dark sky region. This double exposure may have to be repeated a few times to get a better chance of having things fall into place. The night scene shot will need a tripod for the time exposure but the full moon shot can sometimes be carefully hand held as the exposure needed for a full moon can give a surprisingly short shutter speed (would you believe 1/125 sec or 1/250 sec at f/11 on ISO 100 film?). Best to have the moon maybe a bit underexposed so that all the texture shows and the colour comes out a dull yellow-brown and has a ominous feel to it.
Don't forget to restore the camera settings to normal when you are finished mucking about with multiple exposures.
5. Multiple images of person or subject moving against normally lit background. By altering the ISO setting the sum of the multiple exposures will cause the background to be OK but the moving foreground subject will be underexposed except where the subject images overlap. Also the foreground subject will be "transparent". This method is used to put a ghost into a picture by having a clear shot then the second shot with the suitably attired "ghost" in the frame. Judicious use of flash for the subject only may improve the result.
6. Take multiple shots with different zoom settings. This will give a stepped look to the scene as opposed to the streaky effect of zooming while the shutter is kept open. If the scene is lit by daylight then the exposure compensation as noted above is needed, if a night scene then possibly the best effect is achieved by leaving the ISO speed set normally. Experiment.
7. Multiple shots of a still life subject with the lens in focus and then out of focus. This will give a soft blurry edge to the image a bit like having a strong fog filter.
8. Multiple shots with slight camera movement each time, this can give an earthquake or movement look to the photo, or just look plain stupid.
9. Using a dramatic cloud filled sky, focus on a scene and take maybe ten exposures at thirty second or more intervals. The movement of the clouds in the sky will produce different "explosion" effects depending on direction and speed of the wind.
10. Multiple sun or moon. A little maths is needed to find out the best interval time required. The earth rotates 360 degrees in about 24 hours, that is 24x60=1440 minutes, and that translates to 4 minutes to rotate one degree. The sun or moon presents an image of about ½ degree so it appears to move its disk width in 2 minutes. In other words, if you do multiple exposures of a setting/rising sun at less than 2 minutes apart then you will get disk overlap, time between exposures of greater then two minutes will give you discrete multiple suns or moons. Experiment a bit to get the gaps looking the way you want.
11. Confusing shadows. This one may take a lot of time having the camera set in the one place. Shoot multiple exposures of a scene that has lots of strong sun lit areas and strong shadows from tall objects but space the exposures out over many hours. Shadows will point in strange directions. A simple scene would work better here, as a complicated scene would end up a confusing sight with all the shadows added. Keep a "space blanket" or something light and reflective over the camera between exposures so it won't get stewed if you end up in the full sun.
12. Peculiar traffic shots. Try multiple exposure on a road. This would work best with the electronic cameras that can be set up for, say, four multiple exposure, then the shutter fired in fairly quick succession to get the same vehicle "following" itself down the road but in a ghost form as the road or background will show through the vehicle.