If you have point data from rain gages of known locations (which you indicated in a comment), you should be able to interpolate a surface. Which method of interpolation you use is up to you and there are lots of references for determining the best methods and the science/art of kriging (a more involved interpolation method). You can usually get a decent result from the IDW method which is easy to calculate so why not start there?
I'd recommend having your points in a Projected Coordinate System simply because raster processing seems to work better that way (in my opinion).
With IDW you would use your rainfall data as input
(Input points and a field with the data).
IDW link
Using a default for cell size may work well if the gages are evenly dispersed but you can refine this and experiment with the power and search radius settings as well.
Here are some references on the subject of interpolation with precipitation data.
http://popups.ulg.ac.be/1780-4507/index.php?id=10003
http://proceedings.esri.com/library/userconf/proc07/papers/papers/pap_1451.pdf