We want to cut off all leaves that will end up under water in the final arrangement; just bare stems under water. Those leaves will rot and foul the water, which will shorten the life of your flowers.
Use a commercial floral preservative or make one yourself. What you need is some sugar, some acid, and something to kill bacteria growing in the water. The best homemade preservative is half luke warm water and half sugared, citrus-flavored, carbonated soft drink (e.g. 7 Up or Sprite) to which you've added 1/2 teaspoon of chlorine bleach to each quart of solution.
Here's what does not work to properly preserve cut flowers - pennies, aspirin, or cola - Grandma may have done this but they do not help.
Placing The Arrangement
Where you place your bouquet is very important
Keep your arrangement out of direct sun, away from heat sources, and out of drafts.
If you have a suitable place, set your bouquet in a cool spot at night while everyone is asleep. This will help keep the flowers looking fresher longer. A stubby arrangement can spend the night in the refrigerator to extend its beauty indoors. Even a basement will be cool enough to make some difference in the staying power of your cut flowers.
So how long does this stuff extend the life of the cut flowers?
If you put flowers in plain water with nothing else you will keep them nice for 3 to 5 days in most cases.
If you add preservative to the water and cut off the stems under water and that stuff; then you are looking at having nice flowers for 5 to 7 days.
If you change the water every day or two and keep them in a cool place at night you can have blooms lasting 10 to 12 days.