How are aircraft shipped to their customers?
They are flown to their customers by either Boeing or pilots from the given airline. 

As for the Boeing factory its self, the Everett Factory users Paine Field as their runway. If you look closely there is a bridge that crosses the highway and connects the plant to the main ramp of the airport. This appears to be painted for car traffic but is also used for aircraft. The Renton Factory lies adjacent to Renton Municipal which it uses to fly the aircraft in and out there is also a small bridge connecting them over the river. 

Similarly the main airbus factory is located next to Toulouse–Blagnac Airport. Bombardier lies next to Montréal–Pierre Elliott Trudeau International Airport.