Summary of perldoc:

tar -xzvf your_module.tar.gz # one-step decompression
cd your_module_dir
perl Makefile.PL
make
make test
make install # assuming tests are successful
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I suspect, however, that the last stage isn't going to work for you, as I believe you need to be root on the machine to run make install (this would also make DBI available to everyone on that machine.

You may find that you need to load DBI manually into each application you write using either:

use DBI;
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require DBI;
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You'd probably want to try testing things out using a require (which, as I recall, would allow you to roll a custom importation script for debugging) and then, once you know everything is running correctly, switching over to use (which will import the DBI module at compile time).