Quickcast Action can be utilized as follows
1) Begining of the Action Phase - each player may choose to use thier quick cast action at this time, with the individual having initiative going first.
2) After or before the action of a friendly creature - in which case yes it would go back and forth with each exchange of activation.
3) A final quickcast phase- which follows the same rules as the first step.
See pg. 12 rule book!
Hope that helps