Its not too difficult. Just like baseball, you hit the ball, then you run.
Working as a 2-man team with the other batsman, you run back and forth between the wickets (which are spaced 66 feet apart). Running from one to the other is 1 run.
The object of the game is to score as many runs as possible, with the winning team scoring more runs. The job of the fielding side (the other guys) is to prevent the runs from being scored, while trying to get you out.
That much I've got. But there's a lot of technical slang, like "overs" and "centuries" that folks need to know (only some of which I know). The scoring announcing in cricket is very confusing to the uninitated as a result.
And then there's the fact that the number of runs scorred might not matter in a test match if it's not finished in time--resulting in a draw--hence the (to my mind perfectly charming) fact that one can 'declare'--end your side's inning early by your team's choice--so that a draw doesn't result by taking up too much time (and keep an eye on the sky, the five days don't get extended simply because you can't play in the rain). (A tie--very rare--is what it sounds like, both sides have scored the same number or runs when the last batsman is out. A draw is a match ending without winnner because it was not completed.)
(The fact that the crucial stategict decision in a test match is when to decide you've scored enough, and be gentlemanly and let the other side have their inning, while charming to me, is probably the main reason cricket has very little chance of catching on in the US.)
Good luck and godspeed to our team, though.
whats the whole thing about 66 wickets over 4 and all that.