Panning

Arrow keys, middle-mouse button, screen edge (will need to type "/grabinput" in chat first every game if you have multiple monitors for it to work on all edges), or click on minimap. That last one might require changing minimap settings first (space+click on minimap, change "Left-click behaviour").

I'm curious, what had you tried to do?

Try pressing alt and control with the arrow keys. Additionally, a wireless mouse is a handy acquisition for laptop-based players of RTS games.

I've tried playing with a touchpad and only being drunk prevented me from tearing my hair out.