How do you attach cut-out shapes of fondant to a crusted buttercream cake? Any suggestions would be greatly appreciated.

You can brush water on the back of the fondant pieces and just stick them on.

Yep! water works really well!

I always pipe some buttercream on the back of the fondant piece and just place it on the cake. I've never lost a piece of fondant using this method. I'm not a fan of water on buttercream but that's just me.

I have just stuck them right on. That's worked for me.