Magic the gathering number of cards in a hand
You always draw 1 card in your draw step (unless some effect says otherwise), regardless of the number of cards in your hand.

There are card games where you draw up to some number of cards in your hand, but Magic isn't one of them.

Rules: 


  
  Draw Step
  
  
  504.1. First, the active player draws a card. This turn-based action doesn’t use the stack.


The player who plays first doesn't get a draw step in the first turn only (rule 103.7a), after that there is no difference between the player who started first and the other. The maximum hand size for both at the end of the turn is 7.