What do I do if I have zero cards left in my hand at the end of my turn? Do I wait until the end of my turn then draw the usual one card at the beginning of my next turn or do I draw a new seven card hand?
When you get to your draw step, you must draw a single card, unless some effect lets you draw more or less. If you attempt to draw a card when your library is empty, you lose the game.
Even if your hand is empty, the rules remain the same, and you still only draw one.
Here is how the comprehensive rules states it.