shout here means it's on me. e.g cowboy:lets go have a drink Nika; i want to but i dont have money cowboy: dont worry i'll shout you. Nika:o.k lets go. cowboy...

Yes, we say it a lot here in Australia (because we drink a lot? haha). You can also say, "I'll shout you" or "I'll shout this one".

thanks FD owboy...

It means "it's my treat".

roi_g's answer is correct. It means "It's my turn to pay". Just to add though - you'll only find that phrase in England or Australia, not in the U.S.