How do you remove the air that is trapped in the upper portion of the engine?

You vacuum it out using the AirEvac (P/N 04700) from Mityvac. This is a tool that creates negative pressure within the cooling system (a vacuum). By creating this vacuum, it removes the trapped air and refills your cooling system while still holding your system in a vacuum. All fluid will be drawn from the coolant container into the system until it is full. (Ensure you have enough coolant mixture before performing this task.) Once the system is filled the vacuum will no longer exist because the coolant now occupies the void. 

No Air! No problem!