You can either purchase a notebook with scorecards from sports stores, or you can print off scoring sheets from the internet at home. Assign 1 scorecard per team, one for the home team and another for the visiting team. You can find scoring cards online by searching "printable scoring cards" on Google. You can write one name per row, starting with the 1st batter. Fill this out for the "Batter" and "Pitcher" columns. Include other relevant information on your scorecard, like team, umpire, and the date. You can make a separate section at the bottom for bench players, if you'd like. Typically the jersey number is listed first, followed by the players' name, and then the players' position number. In softball, each position is assigned a number in order to keep track with your scorecard. There are other positions that receive alphabetical abbreviations, as well. 1 = Pitcher, 2 = Catcher, 3 = 1st base, 4 = 2nd base, 5 = 3rd base, 6 = Shortstop, 7 = Left field, 8 = Center field, and 9 = Right field. There are also 2 other player positions to abbreviate. Designated Hitter (DH) is the player who only hits for someone who only plays on the field. Pinch hitter (PR) is a player who is substituted to bat for a player in the starting lineup. If the pitcher is hitting, you can include them in your lineup. If not, DH will take your pitcher's spot.

Summary:
Use pre-printed softball scoring cards to score your game. Write out the players' names in batting order. Write down each players' jersey number and abbreviated position.