Collision Trouble

So I'm making a prototype for a game, and I want to add a collision system to it. I have the detection part down:

function checkCollision(rect1, rect2) {
  if (rect1.x < rect2.x + rect2.width &&
   rect1.x + rect1.width > rect2.x &&
   rect1.y < rect2.y + rect2.height &&
   rect1.height + rect1.y > rect2.y) {
  }
}

And I don't want the player to move past the rectangle it's colliding with. If I were to type to type 'player.x += 0' or 'player.speed = 0', it would just stop the player from moving regardless if I press WASD. How would I make it so that my player can't move through objects?