I have a set of data points and would like to add a new column to its attricutes table that has the elevation of where those points are located. Is this possible through a GIS tool? Thank you
This begs the question... it is PointZ data file? If the layer has Z values you can use the Add Geometry Attributes—Help | ArcGIS for Desktop
If it has no Z values, you can manually add a field and add the data yourself. If the data came from another source, like a gps, then there are alternate solutions, should the conversion software not bring elevation over, if the device recorded it.
3d analyst tools
If it is a Point feature ie no Z but you have an attribute with the elevation / height, use Feature to 3d by attribute.
If it also has no Z but you have a digital elevation raster somewhere use Interpolate Shape.