You need to read about capturing matches into the $1, $2, etc. variables. Basically, you need to put what you want to match in parens. Each group of parens is a $N variable in the replacement pattern:

use strict;

my $test = "this is 'inquotes' o'leary";
$test =~ s/ \'(\S*)\' / \"$1\" /g;

print "$test\n";
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It should also be noted that your use of whitespace to find just the "words" will likely fall apart for some cases. There are better ways of doing that. Again, as part of your study, check out zero width assertions, such as \b that matches at word boundaries without actually matching a physical character. Also check out lookahead assertions. In some cases, it can also be as simple as replacing something like your \S non-whitespace match with a character class that excludes quotes.