Probably the easiest way to describe cricket is to say it's exactly like baseball in basics, but completely different in specifics. In both games, teams (11 players in cricket) alternate batting and fielding, trying to score runs when batting and trying to get opposing batters out when fielding.
Most of the similarities end there. Instead of bases, cricket has wickets (two sets of three short wooden poles 66 feet apart). Four feet in front of the wickets are two chalk lines called creases. The cricket batter stands on top of this crease and tries to hit balls thrown from the pitcher (called a bowler in cricket) behind the crease at the opposite wicket.
In cricket, there's no foul territory, no balls and strikes, and the batter always bats with a partner who's standing at the opposite wicket with his own bat. Only one batter hits the ball at a time, but runs must be scored in twosomes.
The cricket batter doesn't have to run when he hits the ball, but if he does, then he and his partner (carrying their bats with them) simultaneously run down over the creases at their opposite wickets. That scores one run. And if the batter hits the ball far enough, he and his partner can keep running back and forth like this, from wicket to wicket, scoring another run each time they switch.
A fly ball deposited into the stands scores six automatic runs (like baseball's "grand slam" home run), a ground ball hit out of the grounds scores four automatic runs (like baseball's "ground-rule double").
In cricket, the batter doesn't come out after scoring a run but continues to bat until the fielders get him out. This is one reason cricket games can take so long. Theoretically, it's possible to finish a cricket game in 20 pitches (this would happen if the first 10 batters on each team got out on their first pitch. The last, or 11th batter, doesn't have to be put out because, as we've said, you can't bat alone.)
The fielding team can get batters out one of four ways. If the bowler can blow a pitch past the batter and hit his wicket (something like a baseball "strikeout"); if the batter hits his own wicket while batting, even accidentally; and if any fielder can catch a ball on the fly (just like in baseball). A fielder can also get the batter out when he's going for runs if he can get to the ball, throw it, and hit the wicket before the batter's reaches his crease (like a ground out in baseball).
A cricket game lasts only one or, at the most, two innings, and can take one or even two days to complete a game. That's because everyone on the batting team must come up to bat and be put out one after the other before the fielding team can bat. When the fielding team comes up, they repeat the process. Whichever team scores the most runs wins.