How do I get the defensive positions to fill in on the scoresheet?
Each team's manager should indicate starting positions on their lineup cards (which the umpire will give you copies of). Fill those in for inning 1 for the players starting the game. (Leave the other players' inning 1 spaces blank.)
Subsequent innings, the managers must give defensive substitutions to the plate umpire, who will pass them on to you. Do not record these substitutions unless you get them from the umpire.
How do I fill in the position for each inning on the scoresheet?
On the AA, AAA, (and starting in 2018) Majors scoresheets there is only a column of half-squares for position:
What do I fill in for "Final Count for Days Rest" for each pitcher on the Pitch Count Tally Sheet?
Note 3 on the bottom of the Pitch Count Tally Sheet explains it in more detail, but a quick rule of thumb is to fill in the number of pitches up to and including the first pitch to the last batter. In the example in Note 3, the pitcher starts a batter on his 18th pitch, and throws 24 total. You can fill in 18 (or 20), to indicate no days rest are required.
What else should a pitch counter know?
Be sure to read all three notes on the bottom of the pitch count sheet. Note 1 recommends switching the direction of slashes between batters, and circling the last pitch of each inning. Note 2 reminds you that you must notify the scorekeeper, head (plate) umpire and both managers as soon as a pitcher reaches their maximum allowed pitches for their league age. (The pitcher may finish the batter they are pitching to when they reach their limit.)