It likely depends on what version of ArcGIS you have. You need to find the minimum and maximum value of the grid. One trick, which works in any version, is to create a constant grid and use it as the zone for a zonal max and zonal min calculation. Now you have four grids: the constant (which you can throw away), another constant grid with the zonal (=global) max in every cell, a comparable min grid, and the original grid. Normalize the original grid with a linear change modeled after this one:
normalized = ([original] - [min]) / Float([max] - [min])
(Float may be needed to enforce rational division rather than integer division when the original grid is in integer format.)