'Shall' is used with the first person : 'I' and 'we'. 'Will' is the equivalent form for 'you' 'he' 'she' 'it' and 'they'. The main use of 'shall' in modern everyday English is for questions with 'I' and 'we', when you are making suggestions or offers. For example: I'm hungry. Shall we go to restaurant? It's the teacher's birthday today. Shall we give her a present? Are you cold? Shall I close the window? Your look bags heavy. Shall I carry them for you? This is the only use of 'shall' which you need to worry about. Other uses which you might come across in older books or in official documents are outdated and/or quite formal, so you will never need to use them.

In American English, lawyers use "shall" when writing laws to indicate that somebody must do something. Other than that, people don't use "shall" unless they are trying to sound British or old timey.