I believe you are referring to time lapse photos. The lens is just left open for longer to give this effect. You will have to check your cameras specs to see if it has this feature.
Simply select the Shutter Priority shooting mode (usually referred to as "Tv"). Then set the shutter speed to something that’s slower than 1/your lens's focal length (eg. 50mm lens = slower than 1/50th of a second). How slow you set it determines the "softness" of the water. (Longer = softer water)
Too bad the camera I use can't go slower than 1/160th, or somewhere in that ball park. I tried to take a slow-shutter picture of water spraying violently from a spigot, and it turned out nothing like I wanted it to.
A ND filter would work if the camera was capable of shutter speeds slower than 1/160th, all it would allow you to do is shoot at 1/160th, with a larger aperture. Since the smooth effect of the water is generated by the length of exposure, rather than the amount of light hitting the sensor/film, I don't think a ND filter would do much good.
When Luke says his camera won't go slower than 1/160 this maybe just for the conditions he was in. If 1/160 is the right exposure at the minimum aperture then forcing it to use a slower exposure will ruin the shot as it can't reduce the aperture to compensate. This is where an Neutral Density filter comes in, as Caedes says. Using this restricts the light coming in to the camera, so instead of 1/160 being the correct exposure, 1/20 will be correct at the same aperture (assuming you use a x8 ND filter). You'll probably also need a tripod. I've just got round to buying an adapter and an ND filter for my Z1 so I'll be experimenting with these sort of shots soon - I'll let you know how I get on, Luke :-)
Basically he said that with the filter, the shutter has to stay open for longer to allow enough light in, so you can acheive the time lapse effect which gives the "silky water" effect you are referring to.
You could also bring the photo into photoshop( if you have it} and soften the water using different filters or the blur tool. Select the water and try different things.