I cover the tiers in fondant. Elevate each one so they are on something a bit smaller than the tier, say a large tin or something. I use an exacto knife at 90º to cut any fondant to exactly the level of the board.
I generally leave them to dry a couple of hours before attempting stacking.
To stack I lift each tier with a cake lifter, not a spatula. I use a lifter, not a spatula, since it tends not to leave a mark at the very edge of your fondant when you slide it out. In any case make sure you use whatever tool you choose at what will be the back of the cake, not the front, since it's easier to hide any boo-boos. I place my left hand near the rear (so actually it's at the front) of the tier I am moving and put it in place. My hand is there just in case, and since I covered it some time ago if I have to move it with my hand it won't leave a mark. You could also use a fondant smoother.