How to check if a LaTeX package has been installed?

If you know the name of the .sty or .cls file from the package, you can do

kpsewhich <filename>

and it show you the location of the file where Latex system finds the file. If kpsewhich doesn't find it, you probably didn't install the files correctly or didn't run mktexlsr or texhash.

Also, please show us the output of

echo $TEXINPUTS

from the commandline.