The Early Offer
Once the final teacher interview is completed, schools would usually send an email with the terms of the contract of your employment, including the salary. It would be prudent to review the contract details. Some important things to remember are the number of holidays, housing allowances, health insurance, and working hours. Certain high paying positions have challenging schedules, while lower paying positions to compensate with excellent bonuses or other rewards. You would have to take these things into consideration since they cost the school and would affect the salary they would be willing to offer.
Once you have taken into consideration the benefits of the position and you are convinced you are worth more than their offer, it is time to negotiate. The first thing is to ask the salary details. The school would then realize that salary was a pertinent factor in your decision.
The Counter Offer
If you are given the salary you asked for, then you can accept the offer and promote your career in teaching. Organizations would not be generous on another round of negotiation. You would come across as materialistic and that would not be good for your teaching career.
The worst case scenario is that they say no to you. Do not worry, it is not the end of the world. You would still be improving your negotiation skills, which would be useful while applying for other jobs in teaching in the future.