How do I stop people reading my iMessages as they come in? I don't want anyone to be able to see from whom I am receiving iMessages or text messages or the content of those messages. 

Can I hide both!?
If you mean from the Lock Screen or Notifications Centre, then
Settings > Notifications > Messages
switch off Lock Screen &amp;/or Notification Centre

.. or if you simply want the content of the messages disabled, lower down the screen [out of sight on this image] uncheck Show Previews - though that will show who sent a message, but not the content.