The most common use of an ND filter is to reduce the exposure for all or part of the image. In the examples above, an ND filter was used to lower exposure in order to use a shutter speed slow enough to blur the water. Because sometimes in bright light you can't get it slow enough without the filter. Graduated ND filters have a portion of the filter shaded and a portion clear. They come in hard or soft and are used to reduce exposure for a portion of the image such as a bright sky. Hard ND filters have a straight line between the shaded portion and the clear portion. These are best when there's a relatively straight horizon or line between the areas of bright and dark. Soft ND filters blend between the shaded and clear areas for images without a straight line between the bright and dark areas. The number-.06,.09 etc.- represent the number of stops of exposure you lose when the filter is on. The higher the number, the darker the filter, and the lower the exposure.
If you want to use graduated filters, I don't recommend a screw-in filter. You can't easily postion them to get the shaded area where you want it. If all you want is to reduce the entire exposure screw in filters would be ok. The Cokin filter holder and square glass or resin filters are preferred for graduated ND filters. They are more versatile with placement and can be used on any number of lenses via the lens adapter rings. One thing to keep in mind when buying ND filters is the subject of color. The N in ND stands for "neutral" but most of the less expensive filters are not neutral in color. They are fine when used for B/W images but can add a color tint to color images. If you can afford it buy the more expense filters to get a more neutral color. The Lee series filters are very nice; but they are not cheap.
Another option for graduated filters is to skip the filters altogether and use your camera's bracketing and a software program to merge multiple images.