Use a corrugated, preferably new, strong box. Gently set the flowers inside, adding extra padding in the empty spaces. Packing peanuts work best, or extra kraft paper if you have alot of empty space to fill in. Keep in mind, the bigger and heavier the box, the more expensive it is to ship. Try to leave 1"-2" between the box and where your flowers are facing up. Add a fragile sticker, and "this side up" sticker if you can, facing up towards the top of your flowers in the box.
FEDEX is recommended for flowers, becuase they are the quickest and most reliable.
USPS is fine, and is more affordable. They also usually have free boxes. Whether you overnight your flowers or are able to expedite them, depending on your location.... please note the golden rule: