DBIx::Class makes this relatively easy, as you can pass additional parameters to a resultset and get back a resultset that will produce a query that matches all of the things you've searched for so far, so you could do something like this:

my $rs = $schema->resultset( 'Users' );

if ( my $year = $cgi->param( 'birth_year' ) ) {
    $rs = $rs->search( birth_year => $year );
}
if ( my $fname = $cgi->param( 'first_name' ) ) {
    $rs = $rs->search( first_name => $fname );
}

while ( my $user = $rs->next ) {
    print "User ".$user->name." matched!\n";
}
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You may be able to use SQL::Abstract for that. You may wind up with something like:

my %where_clause = ();
if ( $cgi->param( 'field1' ) ) {
    # obviously, some validation should be here
    $where_clause{ 'field1' } = $cgi->param( 'field1' );
}
# etc.
my $sql = SQL::Abstract->new();
my ( $stmt, @bind ) = $sql->select( 'table',
                                    [ qw( field list ) ],
                                    \%where_clause );
my $sth = $dbh->prepare( $stmt );
$sth->execute( @bind );
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