No tournaments, but you can play each game multiplayer (some with max of two people, others with max of four).
The main Wii Sports screen has five buttons on the left side of the screen for the different sports (tennis, baseball, etc.) stretching from one end to the other. On the top half of the right side, you have a picture area, so say if you put the cursor over the tennis button on the left, it'd show a picture of tennis in the upper-right half. Then under that, in the lower-right half, you have two buttons. One is for Wii Training where you can train in three different types of modes for each game (fifteen different training games in all), and then the other button is where you take your Wii Fitness Test, which gives you your Wii Fitness Age (20 the best age, 80 the worst). In the fitness test, it just gives you 3 different, and random, tests, whice are all from the different training games I mentioned above.
And that's about all. Different sports have different options, but I'm too lazy (and I don't know all of them) to go into any detail.