Snip the bottom 1 inch off each of the flower and greenery stems diagonally with a sharp knife or wire-cutters. This allows the stems to soak up more water, making the arrangement last longer. Place them in a bucket of water so they stay fresh while you are assembling the arrangement and securing the candle.
Cut the oasis, a grainy, green, sponge-like material used in floral arrangements, so that it is small enough to fit into the middle of your centerpiece bowl. It should be at least 3 inches shy of the top, so that it will not be seen when the flowers are in place. For example, if you are using a 16-inch bubble bowl, the height of the bowl is 12 inches, hence the oasis should be no higher than 9 inches.
Fill the arrangement bowl with water, submerge the oasis into the water and allow it to soak up as much water as it will. Continue adding water to the bowl until it no longer needs to be added, as the oasis is full.
Push the bottom end of the dripless pillar candle into the oasis 3 inches minimum by gently twisting, turning and pushing it into the oasis until you are happy with the height.
Remove the flowers from the bucket and start arranging them in the bowl around the candle. If the stems are too long, you can trim them at an angle again with the knife or wire-cutters. Start with strategically placing the largest blooms first. Place them spaced well apart, you don't want two of the same flowers right next to each other. Next, start placing the smaller blooms into the bowl, spaced similarly to the larger blooms. The idea is to hide the oasis with the stems of the flowers. Don't worry about gaps between the flowers, this is what the greenery that is yet to be added will balance.
Tear your greenery into manageable sections. Greenery is what will fill in the gaps between the flowers and best hide the oasis in the bowl. Ferns such as asparagus fern are pretty to look at and fill unnecessary gaps nicely. As you add the greenery, you may find you need to move some of the larger flowers around to make everything even. You also may find you would like to add more of the larger flowers. There should be greenery and smaller flowers around all sides of the larger flowers, and the arrangement should look relatively symmetrical all the way around.
Step back when you feel you have enough flowers in the arrangement. Look it over and see if the oasis is visible anywhere. It may well be around the base of the candle. There should be enough flowers that they are tight, further securing the candle.
Hide the oasis holding the pillar candle by trimming the stems off leftover flowers and greenery and sticking them right into the oasis holding the candle. This will hide it without compromising the candle. Because the candle is dripless, it will not wilt the flowers.
Double-check the candle to ensure it is buried far enough into the oasis that it will not fall over.