The game rules for Coup are simple, but a turn can get quite involved if there is a lot of counter-acting and challenging, so it's important to keep track of where you are in the sequence.
Here is an example of a complex flow of events.
1. It's your turn. You claim the Captain and declare the Steal action, targeting Fred.
2. You pause to see if anyone wants to challenge your action. Jenny announces a challenge.
3. You flip over one of your cards, showing that you really do have the Captain. Jenny must lose a card.
4. Now your Steal can go ahead -- but Fred, your target, declares a counter-action, saying that he has the Ambassador.
5. Millie challenges Fred's claim, forcing him to admit that he hasn't got the Ambassador after all. He must lose a card.
6. Finally, your Steal goes ahead and you take 2 coins from Fred. This ends your turn.