Am I supposed to just copy the whole module distribution into /tmp (or checkout via svn) and then do perl Makefile.PL && make test

Almost, but you don't have to worry about copying or checking out somewhere else. Generally, from within your development directory, you can do this:

$ perl Makefile.PL
$ make
$ make test
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To cleanup afterwards, run make clean or make realclean. See ExtUtils::MakeMaker for details.

For example, to run verbosely (showing all tests), do this:

$ make test TEST_VERBOSE=1
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prove is another option, but you still generally want to run make to have your modules copied to the blib directory before you run prove with the -b option.