You must have seen Beautiful pics of frozen sea waves , frozen waterfalls and spectacular city scapes with light trails . These are done by exposing the camera for a long time. Where the shutter speed goes to low values like few seconds to insane slow speeds like few hours for a single click .
What you need to Take Long exposure photos,
1.A Camera with manual controls ,
You can use any camera only two features you need is manual exposure controls and a timer for shutter release most of the SLR have this features ,some of the point and shoot cameras doesn't have manual exposure functionality .
2. A Sturdy tripod
Get one which can handle your camera.Stability of your camera matters a lot in long exposure shots, the more stable the tripod the more sharper picture you get. So when ever you buy a tripod always go for the best one you can afford. Its a good investment and doesn't lose it value like camera body .
How to take long exposure shots
Step one
Fix the camera the firmly on tripod , frame the shot by zooming, adjusting height etc as usual,
you can use rule of thirds , symmetrical framing or no rules as you like.
Step two
Once you finalise the frame you can put the cam in shutter priority mode ("TV" in canon "S " in Nikon ) where you can decide shutter speed ie how long the shutter should be open during shot.
Step three
Change the "iso" value to the base one like iso 100 or 200 go for the lowest possible iso to avoide noice whch is more prevalent in long exposure.
Step four
For long exposure photography you have to select slow shutter speed like 1 sec or 5 sec .
Step five
Now put the camera on shutter release timer . putting the camera on timer is to avoid camera shake during shutter button pressing .
Step six
Focus the cam either in autofocus or manual focus at the desired object and press the shutter button . Repeat with different shutter speeds and various "iso" settings to get the desired result .