Fun ways to practice the multiplication tables usually involve games. Multiplication.com has several online games, and it's also possible to use dice or card games to learn multiplication.
For an initial explanation of multiplication, there are some picture books that also show how it applies to real life. "Amanda Bean's Amazing Dream," "Breakfast at Danny's Diner" and "Minnie's Diner: Multiplying Menu" are some math-related books.
Multiplication War is a game that only requires a deck of cards. Two people have half of the deck. They take turns turning over a card. The first person to say the correct product of the two numbers wins the trick. Kings are worth 13, queens 12 and jacks 11.
Muliplication.com offers both single-player and multi-player games for practicing the multiplication table. Cave Run Multiplication is an example of a single-player game in which the avatar runs through a cave collecting coins. Periodically the avatar stops and requires the player to solve a multiplication problem. With Granny Prix, the players who are the fastest in answering multiplication problems get to the end of the race track first.
Damult Dice is another example of a multiplication game. Players roll three dice. They add two dice together and multiply the answer by the number on the third die. The sum is that player's point total. The winner is the player who gets to a designated number first.