How do I update the documentation on someone elses module?
Documentation pages on drupal.org are normal Drupal nodes. You need special permissions in order to edit these nodes. There is documentation on drupal.org about how to contribute to documentation.  

If the module in question includes a README.txt file, then you can submit a patch to the module maintainers that includes the updates. If the module doesn't have a README.txt file, then submit a patch that adds one.