Long exposures are somewhat fashionable on photography at the moment and rightly so! I love the abstraction it can lend to your images, simplifying busy scenes and giving either a great sense of movement or ironically stillness.
You can either get long exposures 'naturally' by shooting in low light or forcing exposure times by using neutral density (ND) filters. These cut the rate of light entering the camera and thereby extend exposure times. ND filters come in a variety of different strengths normally 1, 2 and three stops and more recently the Lee Filters BIG Stopper has proved to be popular offering a 10 stop ND! An alternative is to use a polarizer that can add two stops to your exposure.
There are some very simple steps in getting those long exposures:
Set your camera on a tripod. Obviously you can't hand hold a camera without introducing camera shake for long exposures.
Set your camera at its lowest native ISO setting as this inhibits noise and prolongs exposure.
Set 'Long Exposure Noise Reduction' in your camera (you will find it in the menus) if your camera has this function - it will help reduce noise mainly in the darker areas of the composition introduced and inherent to the sensor in your camera.
Compose and focus your image
Fit any graduated filters needed as with an ordinary exposure to keep highlights in the sky in check.
Make an exposure and check the histogram. ONLY when this histogram is fine should you then use THAT particular exposure time as your bench-mark for your long exposure.
Place the Neutral Density filter over the lens.
If your exposure is going to be under 30 seconds you can use the timer in the camera otherwise set your camera to 'Bulb'. (make sure, if you use a Canon, that the 'f' stop remains the same when you change to Bulb)
Cover the viewfinder. If you don't you will may well get purple or magenta streaks in your image.
Protect the filter set from light glare getting between the filters and make sure you act as a human shield to the prevailing wind as it only take
one gust (usually in the latter stages of your long exposure!) to ruin you image.
Take the exposure using a remote release, again to avoid camera shake.
Very long exposures can tend towards the blue in colour and this can easily be fixed in post processing using the White Balance or Temperature slider adjustment tool.
Long exposures are often used in landscape photography but can also be used in many other situations. You are only limited by your creativity.