use warnings;
use strict;

my $line = '3p3V_MON Trip = 2.713V/2.681V';
if ($line =~ m{ 3p3V_MON \s+ Trip \s+ = \s+ ( [\d.]+ ) V/ ( [\d.]+ ) }
+x) {
    print "$1 $2\n";
}

__END__

2.713 2.681
[download]

That works great!! But... How does the result get into the $1 and $2 strings? (novice here, just want to know how it works)

The 1st set of parens, (), captures to $1. The 2nd set captures to $2. See also:
• perlre
• perlrequick
• perldoc -v '$1'
• YAPE::Regex::Explain

use strict;
use warnings;

my $str = '3p3V_MON Trip = 2.713V/2.681V';

if ($str =~ m{([\d.]+)V/([\d.])}) {
    print "$1 $2\n";
} else {
    warn "Invalid data format: $str";
}
[download]

I don't know about the other portions of the logging, but to me that looks like:

• split on the "=" and look at the right hand side.
• Look for: set of digits, optional decimal point, optional more digits, ending with a "V"

I'd probably use ([0-9]+\.?[0-9]*)V with a /g to grab them all (both).

For a decimal value, I'd use /[0-9]+(?:\.[0-9]*)?|\.[0-9]+/