When you first start the game there are a number of decisions to be made regarding whether or not you will be a witch or a wizard your overall appearance and which house you will start off in.
To be honest, we have not found these to be critical decisions or will greatly affect how the game plays out, so go with whatever you are happiest. You can always alter your appearance and unlock character customisations in the game anyway. BUT you cannot change wizard/witch, and cannot change your house.
Once you have customised your avatar, you start the game in Diagon Alley, just tap the exclamation mark above the characters hear to start the dialogue. Then read and tap through to more text when you are ready.
Don't tap too fast or you may miss critical decision options, and besides, in my opinion the story is the best part of the game.
You are pretty much guided through the initial steps of the game and this is generally how the whole of the game plays, you complete tasks and quests, unlock more of the story, make decisions and answer questions.