You score “runs”. When the batsman hits the ball, they run between the two wickets while the other team try to get the ball back to the wickets (so, pretty analogous to baseball, but back and forth rather than around the bases). The equivalent of hitting a home run is “hitting a six”- if the ball crosses the boundary, the batsman is awarded six runs. The term “hit for six” is a fairly common idiom to express something very strong or complete success (though actually it’s often used negatively, as in “Dave went down with the flu and it really hit him for six”).
While a match is in progress, scores are given in a form like “250 for seven”, which would mean 250 runs scored with seven batsmen having taken their turn.
Cricket is pretty Byzantine though, so that’s about the limits of my understanding.