Cut your sunflowers no more than 2 inches taller than your vase. Sunflowers are heavy drinkers and their stems aren't aesthetically important. Having more of the stem submerged means your sunflowers stay moist and fresh. Snip them with pruning shears.
Fill your sink with cool water. Remove all of the leaves from your sunflowers and hold the end of each stem under the cool water. Cut away the last 1/2 inch of each stem at a 45 degree angle. This ensures the stem stays open, allowing your sunflower to drink.
Fill a tall, heavy-bottomed vase half full of water. Vases with thick, glass bottoms and tall, cylindrical bodies work best. The heavy bottom keeps the vase from falling and the narrow shape clusters the sunflowers together.
Crush two aspirin pills with a spoon and sprinkle the powder in the water. The aspirin acts as a preservative to keep your sunflowers fresher, longer.
Slide the sunflowers into your vase one at a time, arranging the blooms as you go. They should cluster together without crushing each other.