NOOOOO!! Never on, or the batter can be called out! The batter steps up to, but not onto, the plate. The pitcher (who pitches the ball for the batter try to hit), has to throw the ball over the plate to the catcher (who stands behind the batter in the same way that the wicket-keeper stands behind the wicket and the batsman). But in baseball, since there's no wicket to hit or protect, the pitcher has to make sure that the ball goes over the plate and at a height that falls within a certain range. If the batter can't hit a ball pitched through this 'strike zone' three times, he's out.

Bet that made your eyes glaze over.

ETA: it's made of something rubbery. The only time the batter should touch it is when he's on the way 'home', having rounded all the bases. Then he has to touch it without being tagged with the ball or thrown out (as in cricket, pretty much) to score a run.

It's still not as complicated as cricket -- or as much fun.