Where do I input drush commands? I am developing a Drupal 6.28 core website from a PC and was wondering where I would make drush commands to update the Drupal core to 7. 

I am new to Drupal and PC Development, but I assume that it is a terminal command? Can I use the Windows Command Prompt? What directory would I need to be in to successfully run drush pm-update projects drupal-7.
Drush core does not support upgrading from Drupal 6 to Drupal 7 with any of the built-in commands pm-update only supports minor updates.  You'll need the Drush Site Upgrade command to advance to the next major version.

Note that this command has not been tested on Windows; it would probably be safer to run the command in a Linux environment.  Use a virtual machine (e.g. virtualbox) if you do not have a dedicated Linux environment.

Doing a major upgrade from Drupal 6 to Drupal 7 is a serious endevour; the Drush site-upgrade command will help you walk through the process, but it does not do all of the work for you.  The process isn't too hard if it goes smoothly, but you may run into contrib bugs that complicate the process.  An alternative method to upgrade would be to just make an equivalent Drupal 7 site from scratch, and then use drupal-to-drupal migration to move your content over.

Finally, to answer your specific question, there are a number of ways to specify the Drupal site that you would like Drush to operate on, but the easiest and most straightforward way would be to cd to the directory that contains your settings.php file (often sites/default).  You will also need to set up an alias (for your target Drupal site) if you use the Drush site-upgrade command; see the file examples.aliases.drushrc.php for instructions on how to do that.