perldoc CPAN has a FAQ section. Item 1 answers your question.

Update: ++Chmrr has pointed out that this is FAQ #5 in the Perl 5.6.1 distribution version. YMMV depending on your local version of perl and CPAN.pm. ExtUtils::MakeMaker has a more complete list of the installation directories you can set. Use your local perldoc to get the most accurate info on your installed modules.

After Compline,
Zaxo

Yes, you can do this by creating a file named $HOME/.cpan/CPAN/MyConfig.pm In that file, you can specify custom arguments to be added any time that a Makefille.PL is run. By specifying a LIB= or PREFIX= argument, you can make the CPAN module install the lib any place you want. It would look something like this:

$CPAN::Config->{makepl_arg} = q[ PREFIX=DIRECTORY_NAME ];
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Or, if you are working with the interactive shell, you can just skip the config file, and do this from the shell:

o conf makepl_arg PREFIX=DIRECTORY_NAME

Good luck!

Being a non-root user I have tried doing this (installing modules into a directory for which I have write permission), and then adding the directory into @INC with

use lib '/path/to/my/dir';

but this doesn't work with modules for which an older version exists. Perl uses the older version (DBI v1.13 instead of DBI v1.30). Is there a way I can specify the version/location I want used instead of letting Perl pick the one it likes? Or, I guess more specifically, can I specify explicitly the order in which directories containing libraries should be considered for inclusion.

UPDATE: Just in case anyone else should ever have this problem, I found out there are multiple instances of perl installed on our system. The default instance called when I ran  perl Makefile.pl  is in a different location than the one I specified in my script. It solved the problem to re-install the module using  /path/to/perl Makefile.pl  when compiling the module.

Perl should always search for libraries in your directories in the order that they appear in @INC. If '/path/to/my/dir' is the first thing in @INC, perl will look there first.

You might want to try something like this:

#!/usr/bin/perl
use lib '/path/to/my/dir';
use DBI;
use Data::Dumper;
print Dumper( \@INC, \%INC );
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That will tell you exactly what is in your @INC, and exactly where Perl is finding all its libraries.