westinghouse
I don't have the chart in front of me, but from memory:
When all doors are closed and the tug is connected call Operator and tell them you are "ready to move". He/she will invariably say "standby".
5-10s later Operator will tell you to contact Delivery.
Delivery will give you your airways clearance and transfer you to Ground for pushback clearance.
I hope that is useful. I don't like to quote procedures on here unless I have the reference material in front of me, but I'm pretty sure that the above is correct.
All the best
G W-H