Use the lowest ISO rating possible

Obtaining this effect is not that hard with some planning a dSLR camera a tripod and a filter for good measure.  Often a small stable tripod is good for this sort of photography, as you often want to get down low to create a nice affect. You want to be using the lowest ISO possible 50, 80 or 100 if that is the lowest setting. Set your camera to full manual or shutter priority, start with an exposure of around 5 seconds, either use a cable release or infrared remote alternatively you can simple use the cameras timer setting.  Compose your shot and set the timer or use the remote release.

Use the smallest aperture

This again is where digital photography is brilliant the instant feedback of our shot.  One of the difficulties with obtaining the perfect shot is you need a long enough exposure to achieve the dream like look which in turn often overexposes the shot even at the lowest apertures f/22.

You really need a dSLR not a compact camera

Again, this is a primary reason why I say you need to be using a dSLR; most dSLR cameras can achieve apertures of f/22 or even f/32 compared to your digital compact camera with minimum apertures of around f/8 or f/11. Even with small apertures, it is common to still have just too much light to make the shot.
What choices do you have, well you could compromise and go for the longest exposure possible for a correctly exposed shot but chances are it just is not going to be that good.

ND filters

Your best option is a filter and in this cases the neutral density filter or ND, as they are known, these are available in different grades. An ND filter is just a piece of high quality glass that is slightly tinted they come in a range of stops, starting at 1 and equates to a 1 stop of light reduction, it halves the amount of light getting through, and in turn allows for a longer exposure.

ND filters are not that cheap but it is a good idea to have two or three that will keep you in good stead for a variety of shooting conditions. If you can obtain a 10 second exposure and you then use a 1 stop ND filter you will now be able to use a 20 second exposure, if you used a 2 stop ND filter you would obtain a 40 second exposure.

Photo credits
Intro photo by Didierbaertschiger