I've done one two-tiered cake frosted with buttercream and the top tier sat diagonally on the bottom tier. It was a disaster. I kept touching the frosting on the top tier and one of the bottom edges of that tier got icing smashed off it (if that makes sense).. that edge was the one that I laid down on the bottom cake first. Is there an easier way to do this? I've seen videos of how to stack round buttercream-frosted cakes but not square buttercream cakes. Please help!

I'm curious, too. Here's a bump.

You stack squares the same way you do rounds. There's nothing different about the process.

Sounds like your fingers are in the way. Use your icing spatula to lower the cake, and use your hand/fingers less. Place the edge of the cake in place on the bottom tier. With the spatula under it to help hold it up, remove your hand, using the spatula to lower it into place. When you add the borders, you'll cover any smudges that you might have left.

I learned a very handy tip from this site a while back. After you've measured the dowel for the bottom tier, in my case, i use large bubble tea straws, insert them back into the cake leaving about an inch or so out. Then place the 2nd tier on it and slowly let it 'fall', still using a spatula to guide it down. This way you at least have a little more control. Hope this helps a little.