Depends on how you want to be paid or how they want to pay you.
1. Go self employed, pocket all the money and declare it with a self assessment form after each April ( taxed as an employee though i think so 25% ish in total) but depends on your full-time salary (40% bracket etc)
2. Start a company (not as bad as it sounds) and invoice the school (would recommend an accountant to sort out your year end financials though). Receive tax relief on expenses (headsets, charts).
3. Have the school run it through their PAYE system (taxed at source).
Adv and disAdv to all 3 but depends on your circumstances.
Currently I do 2, but I use the company for other purposes also.
I wouldnt work for more than 1 school at any one time, try to find one with lots of students though.