Okay, I know this is a really, really basic question, but I need to ask it. Do you put fondant on the cake while the buttercream is still soft, or do you wait for it to harden up first? I can't seem to find the answer, and I would think that it's kind of important!

I too would like to know the answer to this question. I've tried putting it on right after my crumb coat has set up and I've tried putting it on after I've placed the crumb coated cake in the fridge over night and I've tried putting it on after I've pulled it from the fridge and let it thaw a little. No matter which way I do it, I seem to get air bubbles or have some other issue. Any tips would be greatly appreciated

when I use fondant over buttercream, I have mine firm enough to hold up on the corners, but it has to be soft enough for the fondant to stick to it, otherwise the fondant is just flapping around on the sides of the cake...and you will have a disaster on your hands.
I usually only let my buttercream crust just enough that the fondant doesn't pull my corners down (when you can lightly touch it and not cause a mark). If your buttercream crusts too much and the fondant isn't sticking, I have had luck using a very thin brushing of jam or a simple syrup over the buttercream... or i suppose you could add a bit more icing.

Also... I try not to fondant a cold cake. I have horrible bubbles when I pull it out of the fridge then put on the fondant, whereas, if the cake has had time to come to room temp, the fondant goes on much easier. Not sure what the "actual" rule is, but this works for me.

So, it's a bit of a toss up then. Not so soft that it sinks, but not so hard that it doesn't stick. Thanks! I'm going to crumb coat the cakes, then let that harden overnight, then ice, then I'll color the fondant. That should give me the perfect consistency (since I have to color some 9 pounds of fondant!)

I have tried several timescales with this process, if you cover whilst the buttercream is very soft it tends to result in a very rounded cake. I have found leaving the buttercream coating to set for half an hour, then spraying with a fine mist of water and then applying fondant gives the best result, the buttercream is firm enough to hold itse shape, but you must mist well with water to ensure fondant sticks everywhere otherwise you'll end up with air bubbles. A word of advice, wipe off excess water from board after you mist, otherwise fondant will stick to the board as well as the cake and can drag the sugarpaste down the cake, risking tears.