Wash the empty vase with a diluted bleach solution (2 tbsp. bleach per gallon of water), then rinse it well.
Fill the vase halfway full with room-temperature water.
Add a packet of cut flower food (available at most florists) to the water.
Prune off all of the buds, leaves and flowers that will be submerged while the branches are in the vase.
Hold the cut end of a white flowering quince branch under running water. While the branch is under running water, cut the bottom inch or so off of the branch. Then make a cut through the middle of the base and 2 inches into the stem. Make a second, perpendicular cut in the same manner as the first. Make sure to keep the stem's base as wet as possible while you cut. Repeat for all of the cuttings.
Place the branches into the vase.
Change the vase's water once every 48 hours. Keep the ends of the quince's stems wet in a temporary container while you change the water. Allowing them to dry out will interfere with their ability to draw water and keep their flowers alive.