(Please consult the README to check that you have a new enough version of Perl.)

If you use a new-ish CPAN.pm which automatically follows dependencies, the following should suffice:

$ perl -MCPAN -e 'install MySQL::Diff'

Otherwise ...

You can install MySQL::Diff, as you would install any perl module library, by running these commands:

perl Makefile.PL
make
make test
make install

Note that the test suite will not run properly unless you have a MySQL server which it can connect to.

If you want to install a private copy in your home directory, then you should try to produce the initial Makefile with something like this command:

perl Makefile.PL LIB=~/perl

If you want to use the command-line based front-end mysqldiff.pl, you should copy it to somewhere on your $PATH.