As you'll be using longer exposure times or even Bulb mode, a DSLR or an advanced smaller camera will probably the type of camera you think is best for this sort of technique. However, that's not to say you can't use a compact as many do offer longer shutter speed ranges. As well as your camera, make sure you have a tripod to-hand and you'll need a torch for 'painting' light with. A piece of black card can be useful as you'll be able to create a cone-shape from it to direct light more and translucent coloured paper (sweet wrappers will work fine) can be used to alter the colour of the light you're painting with.
When it comes to the set-up, place your camera on a tripod so you can control the torch with one hand while hitting the shutter button with the other then focus and set the camera on focus lock so that it isn't fooled by the uneven light. If the camera struggles to focus, use your torch to light your subject so the camera can adjust. Any standard torch will do and you can either hold it still or move it around to illuminate different areas of your object. Changing the position of the torch will also prevent hot spots appearing in the image.
It's best to slowly build up the amount of light you paint onto your subject so you don't over expose a particular area. You'll need a long-ish shutter speed if you're not using the B-setting and as a torch has a colour temperature that's warmer than daylight, you could end up with images that have an orange tint. Of course, you may think the warmer tones work but if you don't, auto white balance should be able to remove it or you can always edit your images after if shooting in RAW.
If you find the light isn't directional enough, try using a cone made from black card and secure it to the torch to give you more precise control over it.
Top Images: See how painting the scene with light has improved the image of the mushrooms on the left, adding mood and interest to the shot on the right.