Open - Opens My Computer. This action is identical to double left-clicking on the icon.
Explore - Opens Windows Explorer (not to be confused with Internet Explorer), which is basically just a different way of displaying file trees than the traditional My Computer interface.
Search... - Opens the Microsoft searching menu. Also reachable through Start > Search.
Manage - Opens the general system tools wizard which bundles a bunch of administrative tools into one menu package.
Map Network Drive - Allows you to add a network drive (such as your Pomona userspace) to My Computer as if it were a normal hard drive.
Disconnect Network Drive - Removes a network drive that you had previously mapped from My Computer.
Show on Desktop - If selected, a My Computer icon will be displayed on your desktop.
Rename - Don't like seeing "My Computer" all the time? Change it to something else with this.
Properties - Opens the System Information menu, where you can check all sorts of nifty things (like how much RAM you have, etc.).
Start > Control Panel > Switch to Classic View (left sidebar - ignore if already in Classic view) > Mouse. Under the Buttons tab, select Switch primary and secondary buttons.