Toss the teabag in to the mug. Set up a number of different available distances and have each player choose the distance they want to attempt from, give them a set number of tries or set a time limit. Give them more tries or a longer time if they opt for a further distance, but don't let them change their target once they have decided.

Scoring is, as always, completely arbitrary, you can award as many points as you want for the various distances. Decide how you wish based on the number of players.

If your doing this outside and someone wants to get the bag wet before the throw then let them.

If they make their target you can offer them a chance at a further distance with less time/number of chances. You can even make them wager some of their earned points on an attempt at a further distance.