In a serious bet, you pay money to someone if they've guessed correctly, and they pay you if you guessed correctly. To start a bet, you say "I bet you (some amount) that (something will happen). For example:

I bet you twenty bucks that you can't name all of the states in the United States without looking at a map.

But people also use this form when talking in casual situations just to show that they're really sure of their guesses. In this type of situation, the two people aren't really making a bet. In the example above, it's not clear whether the speaker is really making a bet or not. The other person needs to ask whether the speaker is serious.

To make it clear that you're not really making a bet, you can give an exaggerated wager:

“I bet you a million dollars the Mets are going to lose.”

Or you can leave the amount out:

I bet you the Mets are going to lose.

By the way, when I pronounce "bet you" it sounds like "betcha" or "betchu".