In any given round you are given one of three options:
- Full round action
- Move action and a standard action
- Two Move actions.
You also get an unlimited* number of free actions, and a single swift or immediate action.
Free action: You can perform one or more free actions while taking another action normally. However, there are reasonable limits on what you can really do for free.
Swift action: A swift action consumes a very small amount of time, but represents a larger expenditure of effort and energy than a free action. You can perform only a single swift action per turn.
Immediate actions are swift actions that are not on your own turn.
Using an immediate action on your turn is the same as using a swift action, and counts as your swift action for that turn. (effectively, using an immediate action before your turn is equivalent to using your swift action for the coming turn).
So, yes, they can make a swift action, and then a full round action, with that full round action being a full attack.