use strict;
use warnings;
use 5.010;

my $line = '<suite subfamily="Database Connect - SQL" name="DBMgrTest"
+ family="Databases">';


my $pattern = q{ <suite
                 \s*
                 subfamily="(.*?)"
                 \s*
                 name="(.*?)"
                 \s*
                 family="(.*?)" 
               };



if ( my ($subfamily, $name, $family) = ($line =~ /$pattern/xms) ) {

    #Successful match, and the left hand side of the equals sign
    #is a list, and in list context m// returns a list of the 
    #matches for the parenthesized groups

    say $subfamily;
    say $name;
    say $family;
}

--output:--
Database Connect - SQL
DBMgrTest
Databases
[download]

But that pattern is very brittle. What happens if the attributes are in a different order? Or if there are spaces before or after the = sign? Or if there are single quotes instead of double quotes? HTML and XML are hard to parse, so if there is already a well known module like XML::Simple available, learn how to use that instead.