How do I find matching/nesting anything?

This isn't something that can be done in one regular expression, no matter how complicated. To find something between two single characters, a pattern like /x([^x]*)x/ will get the intervening bits in $1. For multiple ones, then something more like /alpha(.*?)omega/ would be needed. But none of these deals with nested patterns, nor can they. For that you'll have to write a parser.

If you are serious about writing a parser, there are a number of modules or oddities that will make your life a lot easier. There are the CPAN modules Parse::RecDescent, Parse::Yapp, and Text::Balanced; and the byacc program. Starting from perl 5.8 the Text::Balanced is part of the standard distribution.

One simple destructive, inside-out approach that you might try is to pull out the smallest nesting parts one at a time:

    while (s/BEGIN((?:(?!BEGIN)(?!END).)*)END//gs) {
	# do something with $1
    } 
A more complicated and sneaky approach is to make Perl's regular expression engine do it for you. This is courtesy Dean Inada, and rather has the nature of an Obfuscated Perl Contest entry, but it really does work:

    # $_ contains the string to parse
    # BEGIN and END are the opening and closing markers for the
    # nested text.
    @( = ('(','');
    @) = (')','');
    ($re=$_)=~s/((BEGIN)|(END)|.)/$)[!$3]\Q$1\E$([!$2]/gs;
    @$ = (eval{/$re/},$@!~/unmatched/i);
    print join("\n",@$[0..$#$]) if( $$[-1] );

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