I know with a mouse, you can press b in edit mode and then box select using the middle mouse button to deselect vertices (or edges, faces, etc.) How do you do this if you don't have a middle mouse button?
In Blender you really have to have a middle-mouse-button, but if you don't own a 3 button mouse, you can emulate one in the preferences.
- Open User Preferences Control+Alt+u.
- Switch the the Input tab.
- Enable Emulate 3 Button Mouse.
You can now use Alt+Left-Mouse to perform tasks normally done with the middle mouse button.
If you are running the KDE desktop (commonly under Linux), ALT + LMB is a system combination that allows you to move the current Window. Aldrik's answer can work, but you need to first disable (or change) KDE's response to this action.
One way to do this is to disable all system shortcuts for Blender:
Right click on the Blender title bar, and then select More Actions and then Special Application Settings...
Then under the Appearances & Fixes tab: check Ignore global shortcuts, select the Force option, and select the Yes radio button. Save the settings.
The ALT + LMB combination will now act like the middle mouse button in Blender.