I love all the different textures, even though it requires a bit more work than my usual one flower arrangements.
I'm certainly not a professional, so feel free to take my advice with a grain of salt, but when I'm putting together something like this I start by pulling out the largest flowers. In this case, that was the dahlia, the lilies and the snapdragons. I put my trusty flower frog in the bottom of the vase and stick the larger flowers in securely, spreading them out more or less evenly. Then I start adding in the filler flowers, often sticking a stem in and then pulling it out to trim it a bit. It's not effortless for me, because I'm always having to correct and re-arrange, but I do love the process.