1. Be sure that when you're shopping you don't allow yourself to be drawn to flowers in full bloom, they won't last long once you get them home and won't stand up as well to transport and handling. You want to choose arrangements with blossoms that are beginning to open and buds that are showing some color.
2. The next thing you want to check is that they are well hydrated and undamaged. The petals should appear firm and plump, avoid any that appear limp or veiney. Now look over the stems, checking for any that are bent, broken or pinched. The blooms won't last long if they can't get water and nutrients.
3. To be sure the flowers are free of insects and disease you should inspect the leaves. Look for holes where they have been chewed on and any spotty patterns or powdery residue.
4. Finally, check the stems and lower leaves for any signs of decay. If they have been left to sit in unchanged water for too long they may be starting to rot. Make sure they aren't beginning to turn yellow or brown.