We'll confine ourselves to the top of the lineup. If you've familiarized yourself with the position numbers, you'll see that the center fielder, second baseman, catcher, and right fielder are the first batters up. Smith singles to center field. A lot of pre-printed scorecards will have a diamond representing the field in the middle of each box. To mark Smith's single, we'll darken the line from home to first and place a 1B next to it.
Many people also like to draw a line to show where the batter hit the ball.
Lawson's up next and he strikes out swinging. Henry is batting next, but while he is batting Smith manages to steal second. I like to use the player's jersey number for this. It makes it easier for me to keep track of things. Other people use the player's position number.