(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.