How do I create such map from point data?
I am using ArcGIS 9.3 and 10
Both of these solutions require extensions to the standard ArcGIS desktop, such as Spatial Analyst.
If you don't want to interpolate between points, the solution is easy. Simply use the Conversion Toolbox > To Raster > Points to Raster tool to create a raster of your points. You can use the Cell Size field to determine the size of the grid, and you can combine points in simple ways (
MOST_FREQUENT | SUM | MEAN | STANDARD_DEVIATION | MAXIMUM | MINIMUM | RANGE | COUNT).
If you want to interpolate between points, you have multiple options, depending on the results you want. Kriging and Inverse Distance Weighted are two common types of interpolation, but Spatial Analyst comes with others as well.
Depending on what your points actually represent, you may also consider using Point Density or Kernel Density. These would be more appropriate when you were attempting to measure the density of discrete observations, rather than interpolate between scattered measurements.
Look into these, and return if you have more specific questions. There are users here with extensive backgrounds in geostatistics who should be able to handle any problems.