As soon as you start to hiccup, disengage from any conversation. It'll only take a minute but you need to stop talking.
Relax. Sit up fairly straight, with a straight neck, chin up a little to allow easy breathing.
Close your eyes and breathe deeply and calmly, perhaps in a semi-meditation.
Visualise an unblocked and clear airway. This helps to relax your esophagus (the tube in your throat that you breathe down).
Breathe like this until you feel completely relaxed. At some point you'll notice you've stopped hiccuping.