Longer exposure times allow you to capture clouds, water, or other moving objects in a smooth, flowing manner, while maintaining sharpness and clarity on still objects. A neutral density filter essentially allows for this extended amount of exposure time, without altering the hue or color of the image. Adding the filter is equivalent to stopping down one or more f-stops, and allows you to avoid making the photo too hot due to the amount of time the shutter will be open.
If you don’t have a ND or polarizing filter available, you’ll need to attempt these captures in lower light, such as in the early morning or late evening (it could be said that if possible, you shouldn’t be shooting at any other time anyway). Many photographers use long exposures to capture shots at night.
Begin experimenting with very small apertures during the golden hour (the hour before sunset or after sunrise) such as f/22 or higher, and bump the aperture up to f/8 or larger after night falls. You’ll end up with several attempts, since nailing a great exposure is largely trial and error. You’ll also need to play around with exposure times, and this depends on what moving object you are capturing.
Clouds need much longer times to properly capture their trek across the frame of the shot; 5 minutes is a good place to start. Rolling or crashing waves at a beach require much less, sometimes 15 to 30 seconds is enough to create the necessary motion in the image.
Due to the sensitivity of the camera during exposure times of this length, a remote shutter release would come in handy. Anything you can do to minimize shake will help preserve the sharpness of the non-moving elements in the photo.
Finally, be sure to do some pre-planning before actually clicking the shutter; try to visualize what the motion of all elements will be in your composition, including flowing elements (clouds, water, car lights), and still elements (rocks, buildings). This can help you better determine what settings you’ll need to capture the image you see in your mind.