One of the less pleasant aspects of sharing your life with a bird is dealing with the droppings. When the droppings land on the paper at the bottom of the cage, that's fine, but nobody likes cleaning droppings off the floor (especially if carpeted) or off your shirt if you've been holding your bird when he lets one fly.
With patience and consistency, you can teach your bird to relieve himself on command, in a place of your choosing. Young birds seem to pick up the skill most quickly and reliably, but you can teach an older bird new tricks, too.
Start by observing your bird — the times of day he's most likely to relieve himself and the body language he uses just before, such as tail wagging or stepping back. Pick your desired command — "Go potty" or "Hurry up" will do, as will anything, just as long as you're consistent.
When you see your bird getting ready to go or you know it's the usual time he does (such as first thing in the morning), ask him onto your hand (or finger, if he's a small bird) and hold him over a wastebasket, newspaper, toilet, or other "poop zone" (some people use paper plates). Give your potty command and praise him when he obeys — even though the response is just a coincidence at first, of course. Praise and stroking are the rewards for correct behavior.
The larger the bird, the longer the time he can "hold it." Budgies and cockatiels aren't good for much more than 15 to 20 minutes, tops, while large parrots can wait for several hours or more. In emergency situations, some larger birds can even hold it a day or more, but asking them to do so is hardly fair.
And even so, it's a rare bird that's that reliable, so keep paper towels and other cleaning supplies at hand.