In Cairo all visa business is carried out at the Mogamma, a 14-storey Egypto-Stalinist monolith that is rumoured to be closing at some point in the near future.
For visa extensions, head to the 1st floor, and turn right. Pick up a form from the police officers at the table in the hallway, fill it in and return it to the police officers to be signed. Take the form (plus two passport photos and two copies of your passport's visa and information pages) to window 12. Then collect stamps from window 43 and file all back at window 12. Next-day pickup is at window 38. Convert your single-entry visa into a multiple-entry visa (LE61) at the well-signed window on the opposite side the hall.