Here's how the Everything Engine (which runs Perl Monks) handles that.

Each user has a unique ID, stored in the database. Every node I create is marked with my user ID. When I visit a node, if the user ID matches mine, the engine displays a textfield with the node text in it. It also puts a submit button below.

If I were to hit 'Submit', it would perform an update of the node in the database, simply replacing the text that was there before with the new text from the form field.

You will need:

• A database
• Some way of authenticating users -- username, cookie, password, special ID
• Some sort of association of user with text, in the database

It's not too complicated, once you know the secret. I suggest looking at DBI.pm on CPAN, as the database and SQL parts are the only tricky things. CGI::Cookie on CPAN might also be useful.