My love of double exposure photography is a pretty recent one. I was always turned off to this particular genre of photography, because I always assumed it was just a bunch of meaningless photoshop tricks. Once I figured it out, I realized you don't need photoshop at all, and it opened up a new world of double exposure ideas and techniques.
Nikons and Canons both have a Multiple Exposure feature (can't speak on Pentax, Sony, etc. If they do have a feature, it should work the same way.) This feature is based off the idea of making a double or even triple exposure with film photography: Take a photo of a dark figure on a bright background, then expose the next photo, lining it up however you wish with the first photo. Here's a simple photo I've taken illustrating the idea:
I took a dark photo of a bunch of trees (a vertical photo), then took a horizontal photo of the landscape right in front of me right after resulting in a Landscape on Landscape double exposure.
This may look like a clump of meaningless notes (because it is), but it helps me keep track of how to keep all of the numbers in my head. What are these numbers? The key to in-camera double exposure photography is the exposure compensation button on your DSLR. This is how you can easily manage how dark or light your want a photo to be without having to manually tweak the shutter each time through trial and error. While much trial and error is involved, if you keep track of what you're doing it becomes a lot easier.
Let's get specific:
Step 1: Turn camera on and set it to Aperture Priority Mode (On Nikons it's the "A" on the dial, on Canons it's "Av")
Step 2: Compose your first shot, and think about how you want it to interact with your second photo. If you're taking a portrait, make sure the background behind your subject is as bright as possible. Ideally, you would like to pose your model on a cliff up against an overcast sky. (Fortunately, I live on a mountain.) If this isn't possible, just make sure your figure is in dark contrast to the background.
Step 3: Set your exposure compensation. If your subject isn't dark enough and the conditions aren't positively perfect, that's okay. The whole reason you change the exposure compensation is to differentiate the two exposures. Play around a bit. Try a low compensation and work up from there. If you're shooting a person like my first photo above, set your camera's exposure compensation to 0.3+ for the first photo, which will underexpose the photo a tad. For the next shot, change it to 1.3+. If you got the desired affect, that's the setting you want. If not, try 0.7+ to 1.7+. You can always play around.
Just remember, if your subject is dark, the content of the second photo will show up on that dark area. The bright areas will always cut through the second layer, and your second layer will not overlay on that bright area. That's the reason you need exposure compensation (not all the time, but you will if it's a sunny or bright area), to darken the image as little or as much as you need.
If you ever browse Pinterest, you probably are pretty familiar with double exposure portraiture. For a while, that's a pretty good start, but there's so much more. Take the above couch on fire photo for instance. For this one, settings weren't as important due to the lighting conditions and the content of the photo. Earlier, I mentioned that you want a bright background against a dark figure, however I did the opposite for this shot. It was around midnight, and I lit a bunch of newspapers on the grill. Obviously, fire supplies enough light, and it being night was completely dark outside. I didn't even have to deal with exposure compensation at all. I took the first photo of the fire, then came inside the house and did what I could to line up my couch with the fire photo I had just taken. (Canon has a sweet feature that helps you line up double exposures with live-view. Nikons, unfortunately, don't have this luxury.) That's it.
Once you figure out the basics of what gets you to a double exposure photo in any condition, your possibilities are endless. You will learn that you aren't limited to double (or even triple) exposure portraiture, but you can double expose anything you want. Take a photo of a street, then take a photo of the same street again, but on its side. Play around with landscape on landscape, or portrait on portrait (I've had creepy results with this one), or even portrait on landscape on portrait again. The things you can achieve with this feature is astounding. I think the most rewarding part of taking in-camera double exposures is in the end, when you blow your friends minds by telling them you didn't use photoshop.