Upon receipt of your fresh flower delivery, you really should re-cut the stems before you put them in the vase to make sure their vascular cells are wide open to take up water.
Always cut the stems at a sharp angle using a knife if possible, or very sharp scissors.
Place the flowers immediately in clean water, or they'll dry out and you've defeated the object of cutting. Make sure there are no leaves sitting below the water line, as not only will they rot and release harmful bacteria, which kills flowers, but they'll also consume vast amounts of the nutrients in the flower food which need to get up the stem to the flower head.
To maintain the look of your flowers, repeat the process 2 days later, especially during summer time, removing any wilting or dead flower heads so that the water supply is sent to the flowers still blooming or, in the case of multi-headed varieties, still to open.