No leaves in the water
Remove any and all leaves that are going to touch the water in the vase. Any leaves that end up in the water can start to rot and release bacteria into the water, which are bad for the flowers.
Put the bouquet in a vase as soon as possible
Once your bouquet has been delivered (or you have come home from the florist), make sure to put it in a vase as soon as possible. Use lukewarm (not too hot, not too cold) tap water to fill the vase and add the right amount of plant food (your bouquet will come with plant food; check the packaging to find the right ratio).