Cut at least half an inch off your flower stems before putting them in a vase or changing out the water each time.
If your flowers are sitting out of the water on the journey home, the ends of the stem will typically dry out, and the cells die, making it hard for the flowers to absorb water. The best thing you can do then is cut a little off the stems before putting them in the water again; the fresh tissue will suck up the water much more efficiently.
You should also trim the stems again when you change the vase water a few days later, remove the tissue that may be breaking down, and expose the fresh tissue again to absorb more water.