Select your flowers, greenery and bucket according to what you're using the arrangement for and where you plan to display it. Gather your supplies in your garden, kitchen or another spot where you have plenty of space to work and easy access to running water.
Clean the bucket and insert a trash bag, or other plastic bag. Arrange the bag so it covers the bucket where the water and flowers will touch, but won't be seen. Fill the bucket 1/2 way with cool -- not cold -- water and flower preservative. Set up a grid using waterproof tape inside the bucket just below the lip, or insert floral foam that has been pre-soaked to hold your flowers in place as you begin building your arrangement.
Choose the flower, or flowers, you'd like to make your focal point. Pick a single flower to use as the center or a couple of flowers to mark the back of the arrangement, depending on where it will be placed, and cut the stems. Place the stems under cool running water as you cut them at a diagonal angle. Build up the stems for height if necessary.
Cut and place each flower, one at a time, until you are satisfied with the way the arrangement looks. Place your main flowers first, then any smaller filler flowers. If you need to bunch filler flowers together, try using a rubber band to hold their stems in place before placing them in the foam or grid.
Add your greenery to fill any empty spots or for contrast and to give your fresh flower arrangement a more natural look. Walk around the arrangement to see it from all sides, then place it where you want it if possible. Add any flowers or greenery, or take any away, to achieve the arrangement you desire.