Could someone explain how the feat Intimidating Prowess works (standard action? Free action? Swift action?) and provide an example for a hero with 22 Str and 10 Cha? The feat benefits reads "Add your Strength modifier to Intimidate skill checks in addition to your Charisma modifier."
It works as per the standard Intimidate Rules.
Intimidating Prowess merely allows you to use your Strength modifier in addition to your Charisma modifier when making Intimidate checks. In your case that would be +6 from Strength and +0 for Charisma. It does not grant any new types of actions or otherwise modify the existing uses of Intimidate.
Please review the Intimidate rules for Coercing, Demoralising and Influencing found a the link as it is too significant a text to reproduce here. If you have further queries about how Intimidate works, it might be best to raise them as a new question.