Visualizing a three dimensional field of data points is more challenging than 2D for two reasons: First, producing surfaces to represent data values is no longer easy, since there isn't a free dimension to use. Second, data values tend to obscure each other, making it harder to see relationships in the data.
Point fields, as described above, can be used to visualize 3D data fields. If the point density is high, points can be rendered with transparency, and sorted from back to front. This makes the obscured points more visible. See Section 12.2 for details on transparency.
Another technique is to use volume visualization techniques to view the data. This technique is especially useful for very dense datasets. See Section 16.2 for details.
Another method is to calculate isosurfaces from the dataset. Data points with similar values can be connected together with a tessellated surface. These surfaces, like point fields, should be drawn partially transparent, using alpha blending, and rendered from back to front. Each isosurface can have a separate color, to make them easier to distinguish. See O'Rourke's book  for ideas on generating the iso surfaces.