If you're having trouble in the beginning, just follow these easy steps:
1. Focus on raising discipline, to the exclusion of all else. Get the stat to 20 or higher (30 is a good number to give yourself a bit of a cushion). Once the stat reaches 20, grades will no longer drop. Don't worry about grades themselves, as you will build these up gradually as the game unfolds.
- Quickest way to raise discipline in the beginning is to teach classes, then punish the offending girl in front of the class. This will give you 2 discipline points per class. Do not punish her after class, as this won't do anything for your scores. Teach classes twice a day (do NOT teach sports or monitor the halls, just focus on discipline). Don't worry about popularity or whatever; that will come with time. If done right, you'll gain 4 discipline per day, and grades will be stabilized by the end of the fourth day or so.
2. Train Miss Potts at night. Every time you possibly can, go to Miss Potts' apartment at night and train her to be a better disciplinarian. Until she has proper training, she'll be a liability as her failure to keep her class in line will cause you to lose 1 or 2 discipline points a day. Just keep at it and eventually she'll improve to the point where she can more or less keep the class in line. She'll still occasionally have the odd slip, but the loss will be much more manageable.
Once you meet these two objectives, the game really opens up and gets a LOT easier. Good luck and have fun!