Hi, I would like start primary school, please let me know the what is legal procedure and formalities?

There is only one legal formality which you must follow in begenning. That is registration. You should form a educational society and get it registered under "Societies Registration Act 1860". At a letter stage if you want to enhance the level of classes you need to take recognition from competent authority from state education department. In UP school upto 5 standard are not required to take an recognition.