Long Exposure shots can either turn out beautifully or turn out looking terrible and you'll want to burn them. (don't because you can then learn from your mistakes) It'll take a lot of practice to get a good long exposure shot on the first try and even then you'll sometimes make mistakes or get just done right bad pictures.
Step 1: Step 1: Starting Out
To take a long exposure photo you first need to go to your manual setting on your camera, it'll often be marked just with an M. Once there, there will be a ton of settings that you can change but the only ones we want to play with are Shutter Speed (1/x) and Aperture (Fx).
Step 2: Start Playing
Now that you know what parts to play with, play with them. Try leaving the Shutter Speed alone and just play with Aperture, get a good feel for what it does. Then reverse it, leave the Aperture alone and play around with Shutter Speed learn what playing with that does. Now to make a Long Exposure picture you're going to need to have a plan, are you going to be playing with light or figures?
For Long Exposure playing with light go to step 3.
For Long Exposure playing with figures go to step 4.
Step 3: Playing With Light
Playing with light is easier when beginning because you can leave the Aperture alone and just have a long Shutter Speed. You're going to need to be in a dark room or else the extra light will make your picture look not as nice. So you're in a dark room, you've got coloured or regular lights, and got your camera on a tripod with a long Shutter Speed. Now once everything is ready, hit the button on the camera you'll hear the click and then start moving the lights around in the air. Once the click sounds off again you'll be out of time for more light drawing. Go back to your camera and look at the finished product.
Once you get the hang of that you can go outside with a cheap whisk, steel wool, an old leash or rope, and a light. Put the steel wool into the whisk, attach the whisk to the leash or rope, and then light it on fire (I recommend having a friend there to push the button for you). Once you hear the click start swinging that whisk around and around, BE CAREFUL AS SPARKS WILL FLY.
Step 4: Playing With Figures
Playing with figures is a little harder when done in a dark room because you can't see where you're going. It's much harder even when you do it in a dark because you have to adjust the Aperture to factor in the natural light.
When doing it in a dark room it's the same idea as playing with lights except you're going to turn the light off when you're switching between movements or positions. You'll turn the light on when you're ready for the camera to record the information.
When doing it outside you need to lower the Aperture a lot but you won't need to worry about turning the light on and off (unless you're a god and can turn the sun on and off).