Zendoku provides you with two choices at the beginning. You can opt for Zendoku, which is the adventure option, or you can opt for Classic Sudoku. Honestly, if you're looking to play normal sudoku puzzles, I'd recommend one of the other sudoku clones,
Sudoku Fever for instance. The reason I say that is that
Zendoku doesn't provide a "pencil in" functionality, which is something that I use heavily. When you do choose to play it, the Classic Sudoku Mode provides you with the opportunity to learn how sudoku is played if you're one of the people that's never seen or heard of it. It also lets you play Sudoku (with the numbers only) either timed or un-timed.
If you're bored with normal Sudoku and you're looking for something just a little more challenging, choose the Zendoku Mode. This mode is where Zendoku really sets itself apart from the other Sudoku games. At the start of it, you're given your choice of 10 playable characters. The bottom 8 players all have a different quest to go on. Choose one, and you'll play against the other seven players first, then your master. After you've beaten all of them, you'll have seven more unlockable characters to play against before you finally get to take on the last opponent to earn your grade of Doshu. After you beat each of those seven, they're unlocked for you to play as.
When you are in a battle, Zendoku has made it much more interesting than just playing Sudoku against someone. Each time you complete a column, row, or box, as I said before, you throw an attack at your opponent. The attacks are like something you'd see in WarioWare Inc: Mega MicroGames. You have a variety of quick things to perform, some of which even require you to blow into the mic. While you are defending against these attacks, you can't work on the Zendoku puzzles, so it makes it much more difficult for you to beat your opponent. When you want a break from your quest, you can also choose to play in Zen Mode, Attack Box, or Multiplayer Mode.
The top two characters you can choose are masters - they already have a grade of Doshu, so if you choose them, you don't have a quest to go on. The seven unlockable characters also do not have quests. With these characters, you can only play in the Zen Mode, Attack Box, or Multiplayer Mode. Zen Mode allows you to play Sudoku using symbols instead of numbers in a relaxed manner to try and obtain the highest score possible. You'll notice that all of Zendoku Mode is played using symbols: a panda, a flower, a temple, a sumo, a yin-yang symbol, a parasol, a heart, a snake and a sword. Attack Box allows you to practice blocking any of the attacks that your opponent throws at you. Finally if you want to play against another player, you can choose Multiplayer Mode.