How do continuous effects interact with the stack, your hand, and other zones?
The creature card would have 1 power and 1 toughness in all zones other than the battlefield


  609.2. Effects apply only to permanents unless the instruction’s text states otherwise or they clearly can apply only to objects in one or more other zones.


The only things that can change a creature card's power/toughness off of the battlefield are Characteristic-Defining Abilities, like what Tarmogoyf has.


  208.2a The card may have a characteristic-defining ability that sets its power and/or toughness according to some stated condition. ... This ability functions everywhere, even outside the game. ...