Dahlias are very exuberant and seduce the eye, so it is better to get playful than to try to control their shape in a static arrangement. Use one color as a base, playing with another on top -- it's almost impossible to go wrong and you'll get a gorgeous piece.
Cover top of vase with tape in a grid formation. This helps create volume and balances the weight of the flowers on top of each other so the ones on the bottom don't get smashed. It's also helpful to hold the flowers in place when the vase isn't very deep.
Select dahlias that are not too closed or too open. Make sure the petals don't come off easily, and strip the leaves from the stems.
Choose dahlias from the pile and start to cut and arrange the flowers within the grid.