You can find out about the location of a module with

$ perldoc -l Data::Dumper
/home/moritz/perl5/perlbrew/perls/perl-5.14.1/lib/5.14.1/x86_64-linux/
+Data/Dumper.pm
[download]

Is there a way to execute the perl program when I know the place of the .pm file?

There are various ways to adjust the module search path. See perlrun for the complete list.

But it sounds like you really want a proper module installation with the CPAN module/program.