Gemma is out of her cage a lot during the day. We have polar fleece fabric that we keep along the back of the couch where she usually hangs out (it sounds a little gross but if you let it dry and then it flakes off easily before laundering). She will usually poop before she flies to a new location so as long as we have her regular perching areas covered then the rest of the house is pretty safe. She does spend quite a bit of time with my shoulder as her perch and she will poop on me too....again a piece of polar fleece worn like a short cape protects my shirt. I've been meaning to make a more tailored collar that I can wear that has a button and just covers my shoulders but that will have to come later.
As Dona said, morning poops are bigger and once she's out things are more manageable, watch out for cherry and blueberry poops....those will stain!! I also make sure that she has areas near her perches to get snacks and water, she doesn't often want to go to her cage once she's out and we want to keep her hydrated in the heat.