aastex.cls file has to be copied anywhere. There is a "make install" capability for Unix systems, but one has to have the installation directory properly identified in the Makefile, and of course proper permissions are required.
In the Makefile for AASTeX:
Set INSTALLDIR to the directory that aastex.cls should be installed in. It would be canonical for it to go in the
tex/latex/misc area. So you probably only need to change the leading portion of this, once you know where your texmf installation is rooted.
If you have tetex installed, you can run "texconfig conf" to see what TEXMFMAIN is.
When the INSTALLDIR parameter is set correctly in the Makefile, you can just type "make install" in the usual way. You must have the necessary write permission in the system area where LaTeX files are installed.