They are called "mallets", also referred to as pushers, strikers, paddles or goalies.
For commercial or home use, these mallets feature comfortable handle for easy grip. They usually come in with felt on the bottom.
Basic Rules of Play
1. The first player to accumulate seven (7) points wins the game.
2. When the puck enters and drops inside a player's goal, the player's opponent receives one point (unless play had been suspended by the referee or the offensive player had committed a foul during or prior to the shot.)
3. After each game, players will alternate tablesides.
4. The player scored upon receives possession of the puck for the next serve.
5. A player may hand serve the puck only after it has entered his goal.
For complete air hockey rules, go to www.airhockeyworld.com.
Learn Tips and Techniques for Winning Air Hockey from Bubbleairhockey.com.