The American Horticultural Society describes two ingredients necessary for an effective cut-flower preservative: citric acid and table sugar. Table sugar is similar to the food plants produce during photosynthesis, and sugar gives them nourishment -- even away from the sun. The citric acid helps keep the plant's vascular system from getting clogged, enabling the plant to take up water and sugar more efficiently.
Aspirin is absolutely not an effective preservative, according to the University of Minnesota Extension. Alka-Seltzer may help somewhat, as one of its active ingredients is citric acid, which would facilitate the uptake of water. Lemon-lime sodas are recommended by both the National Gardening Association and the American Horticultural Society as useful preservatives. Commercially available preservatives are available and are marketed just for cut flower use.
Properly cutting your flowers is as important as adding preservatives to the water. Cut them early in the morning while they are still dewy, or snip them late in the evening. Wipe your shears down with rubbing alcohol to clean them before cutting the stems. Place the flowers immediately in warm water to prevent shock.
Recut the stems at an angle once you placer them under water. This prevents any healing that could close the cut stem. Prior to arranging the flowers, leave them for a couple hours in a dark, cool place in a container of warm water to encourage them to take up water. Arrange the flowers in warm water, and place the vase in a cool place, away from direct sun or drafts. According to the National Gardening Association, the best preservative to add as you arrange the flowers is 1 cup water, 1 cup lemon-lime soda and 1/2 teaspoon of bleach.