I installed the aastex.cls file in the proper place, but my LaTeX system still can't find it.
Modern TeX installations often have a cache of all available files. This cache has to be updated after new files are added in the directory hierarchy.
If you have teTeX, you must type "texconfig rehash" to update the necessary table - this takes proper permissions.
If you have a TeX installation other than teTeX, you will have to explore its instructions for installing extra packages and for subsequently updating the cache.