The best time to trap the queens is in spring when they emerge to start building their nests. A large number of queens can be trapped in this way. Commercial traps are available, but it is not difficult to make your own.
Set up traps for the rest of the season, just as for wasps.
This is a relatively new trap. The goal is to electrocute the hornets when they are hawking around the hives. This is quite expensive, but you can make your own (Spanish).
Apishield is a simple mechanical device that sits under the hive floor. The hornets think they are entering the hive and become trapped in the chamber, from where they can be removed and destroyed.
The Jabeprode Trap (French) is a plastic box that has a separate attractant tank to entice in the hornets. It is quite big, so that there is little chance that it will fill up even if there are large numbers of hornets in the apiary.