I haven't found explanation of how to upgrade this shell to 8.x for drush itself not a module using drush and the site is on Drupal 7.x site. I'm fairly new to all of this and do know how to use drush but was wondering if I should keep this shell updated. I saw there are versions 8.xx that work for Drupal 7 but didn't see instructions on updating. The version running is 8.0.x.dev so I'm guessing I should update to current 8. Version. Thanks in advance.
First of all, Drush is not a module. It is a shell companion tool for Drupal sites so that you can (for example) use the command line to download and enable modules; clear/rebuild cache; check site info; etc...
Its also worth pointing out that Drush 8 does not care what version of Drupal you are using. In fact you can use the same drush installation with lots of your sites.
If you are using Drush for just the basics you don't have to be too vigilant about keeping it up to date, but of course it is always a good practice to do so.
That all said: this question has been asked/answered here: How do I update Drush to the latest available version?