Usually I stop what I'm doing, stand still with my legs apart, hands on hips, and push. Squatting down slightly sometimes helps get things started, after which I can usually carry on with whatever I was doing, especially walking, as it might take five or ten minutes before I'm completely finished and ready to change. I can sometimes do it without interrupting my activities, although anyone who has had a toddler would probably recognise the posture and signs of effort and concentration for what they are. If the need arises while I'm sitting down there's not much point trying unless I can stand up; e.g. if I feel the need while driving, I will often fill the nappy the moment I get out of the car. In bed, I lie on my back and pull my knees up.
My favourite is probably going while I walk, especially if it's a big, firm one. The body movement helps ease things out gently, without any straining or effort, and being able to take my time over it without having to stop is a convenience that only a nappy can provide.