Hmmm. It works great for me. Are you certain that you made the correct changes and no others? Before my changes, the output is:

This program will ask you to type in two numbers and then add those nu
+mbers together.
It will then display the problem and the answer in word form.
Type in a single digit number between one and four, or type done to ex
+it.
2
Type in a single digit number between one and five
4
Use of uninitialized value $sum in concatenation (.) or string at ./su
+m2.pl line 23, <STDIN> line 2.
Four plus four equals
Type in a single digit number between one and four, or type done to ex
+it.
done
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Notice how I input 2 and 4, but it only saw 4 and 4. That is because you were using </c>$userin2</c> in your return. After the changes, the output is:

This program will ask you to type in two numbers and then add those nu
+mbers together.
It will then display the problem and the answer in word form.
Type in a single digit number between one and four, or type done to ex
+it.
2
Type in a single digit number between one and five
4
Two plus four equals six
Type in a single digit number between one and four, or type done to ex
+it.
done
[download]

Here is the altered script. The only changes are on lines 20 and 32 (also 2nd subroutine is commented out).

#!/usr/bin/perl -w
use strict ;
my (@a, $userin, $userin2, $sum) ;
@a = (1 .. 9) ;
print "This program will ask you to type in two numbers and then add t
+hose numbers together.\nIt will then display the problem and the answ
+er in word form.\n" ;
$userin = 0 ;
while ($userin ne "done") {
    print "Type in a single digit number between one and four, or type
+ done to exit.\n" ;
    chomp ($userin = <STDIN>) ;
    if ($userin eq "done") {
        last ;
    }
    print "Type in a single digit number between one and five\n" ;
    chomp ($userin2 = <STDIN>) ;
    if (($userin =~ /^[^1-4]$/) || ($userin2 =~ /^[^1-5]$/)) {
        print "I do not understand\n" ;
    }
    else {
        $sum = ($userin + $userin2) ;
        $userin = ucfirst (numtoword($userin)) ;    #was: $userin = (f
+irstnumtoword($userin)) ;
        $userin2 = (numtoword($userin2)) ;
        $sum = (numtoword($sum)) ;
        print "$userin plus $userin2 equals $sum\n" ;

    }
}

sub numtoword {
    $_ = shift ;
    my (%nums) ;
    %nums = ("1"=>"one", "2"=>"two", "3"=>"three", "4"=>"four", "5"=>"
+five", "6"=>"six", "7"=>"seven", "8"=>"eight", "9"=>"nine") ;
    return $nums{$_} ;    #was: return $nums{$userin2} ;
}
# sub firstnumtoword {
#     $_ = shift ;
#     my (%nums2) ;
#     %nums2 = ("1"=>"One", "2"=>"Two", "3"=>"Three", "4"=>"Four", "5"
+=>"Five", "6"=>"Six", "7"=>"Seven", "8"=>"Eight", "9"=>"Nine") ;
#     return $nums2{$userin2} ;
# }
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Also, it would be more readable to write your subroutine like this:

sub numtoword {
    my $digit = shift;
    my %nums;
    %nums = ( "1"=>"one", "2"=>"two", "3"=>"three", "4"=>"four", "5"=>
+"five", "6"=>"six", "7"=>"seven", "8"=>"eight", "9"=>"nine" );
    return $nums{$digit};
[download]