Wash the vase thoroughly with warm water and a squirt of dishwashing liquid. Rinse the vase well and dry it. This slows bacterial growth once the fresh flowers are in the vase.
Remove old, damaged or dead leaves and any that will be beneath the water level in the vase. Rinse off any dirt on the stems. This is not necessary with silk flowers, but do remove any foliage that is beneath the rim of the vase.
Cut the stems of each flower with a sharp knife, pair of scissors or a wire cutter if using silk. If they are fresh flowers, cut them on a slant so they'll absorb the water better. Do not cut them too short; you can always clip them shorter later if necessary.
Pinch off a piece of florist's clay -- about the size of a quarter -- and put it into the bottom of the vase. Stick your oasis or a metal pinpoint frog to the clay. Craft and hobby stores and florist shops have these items. This step is not necessary if the vase has a narrow neck; it will hold the flowers in place on its own. (see ref 1)
Place the flowers into the vase one at a time. Aim for a triangle shape if the vase is tall. Create a half-circle mound for the bouquet if the vase is more of a shallow, bowl shape. Place larger flowers around the rim of the vase and taller, smaller ones in the center.
Utilize the varied colors of your flowers by alternating them throughout the bouquet. Another idea is to place greenery and one color of flower around the rim edge of the bouquet, such as white daisies, and position another color, such as pink roses, in the center to give a more formal look.
Fill the vase about 3/4 full of lukewarm water, if using fresh flowers. Add a few drops of chlorine bleach to the water if you do not have a floral preservative. This prevents growth of bacteria. (see ref 2) Be sure to check the water level every couple of days, and refill it once it lowers. Skip this step if you are using silk flowers.
Tie a narrow decorative ribbon around the neck of the vase before displaying it, if you desire. Coordinate the ribbon with the colors of the flowers.