Each peony stem usually has 5 to 7 flowers. In disbudding, you remove all but the top bud, as soon as the little side-buds are produced. Don't leave it too long or you will defeat the purpose. All the energy that was to go to 5 to 7 flowers is now reserved for that one bloom. Often disbudding provides amazing results.
Cut flower stems containing buds which are just starting to open, preferably in the early morning.
Be sure to leave 3 to 4 leaves at the base of the flower stem for the plant. The peony at right looks healthy enough, but it is pretty clear that it's falling over. Support peonies with special, circular 'peony rings', tomato cages, or individual garden stakes. In the example given, a large tomato cage, inserted into the ground as the shoots are extending in spring, would have done the trick. It is not always necessary to stake, and floppiness of stems has alot to do with their culture and the variety you select.