My birds fly loose in the house most of the time. Cheeky GCC has good manners and will usually fly to her perch to poop. She also does not like the feel of most fabrics and doesn't enjoy sitting on the sofa, chairs, ect. She pretty much sticks to her stands, peoples' laps, and a few wooden chairs. I never had to teach her not to fly anywhere; she is naturally a little cautious and prefers to stick to familiar spots.
Sammy the budgie has typical dry little budgie droppings that are not messy, if he poops on something, it's just a matter of brushing it to the floor and sweeping it up later.
Kiwi the linnie is the 'problem pooper' as he has very large, messy droppings and refuses to be trained in any way or to even give any advance warning. He used to have a bad habit of flying onto the lamps in the living room. He didn't seem interested in them, but for some reason, he was drawn to them. I tried all kinds of things, including draping toilet paper over the lamps (in the hope it would drift around in the wind produced by his wings and scare him from the lamps) - the end result was he'd still try to land on the lamp but would often slip and fall. Eventually all that could be done was to just run over and remove him from the lamp every time. It was kind of annoying but he has very gradually stopped landing on the lamps quite so much. Now when he wants to fly to that side of the living room, he will usually go for the sofa instead, which is a compromise we're pretty happy with (that sofa is 100x easier to clean than a white lampshade).