Arranging branches in a centerpiece means working with more empty space, as your focus won't be on filling in gaps in a vase as you would if you were using bunches of flowers. The spaces between the branches or between any items placed on them are as much a part of the design as the branches themselves. With this in mind, it makes sense to select a simple vase, bowl or other container that won't interfere with the statement you are trying to make with the branches. The vase can also become an extension of the design by picking up colors, textures or configurations of the branches. There are no hard or fast rules, as the shape, size, texture and color of the branches will dictate what type of container will best suit them. As with any other type of design, experimenting is key, and you'll know what works and what doesn't when you see it.
For more exotic centerpieces, low shallow bowls are a good choice. For upright presentations, the choices include cylinder vases, bottle-shaped vases, round globe vases with narrow-rimmed openings that provide stability, lattice-work styles that provide openings through which to view the bottoms of branches, and tall narrow stylized vases made from natural woods. Tall narrow clear vases with straight or slightly tapered sides offer a view of branches from top to bottom, and can provide interesting contrast if the tops of the branches hold berries, dried leaves or other objects.
You could create centerpieces from branches culled from your own garden or yard or you could purchase branches specifically grown for this purpose from a retailer. Finding your own provides a broader range of choices, as you will need a good eye to spot branches that would both generate interest and enhance your decor. It's important to remember that, like the flowers you pick yourself, freshly-picked branches are perishable and will need to be dried or treated to extend their life. Deciding on a vase goes hand in hand with selecting branches. If you just want to group a few straight branches together, a tall narrow clear vase is a suitable choice to expose as much of the branch as possible. Branches that are more gnarled and twisted are best displayed anchored to more shallow bowls or other vessels.
Branches can be used in dry or wet centerpieces. When placed in water in tall clear glass vases, many branches continue to bloom or produce leaves as they would if left in the garden uncut. For example, forsythia branches picked early in the spring can be forced when placed in water and the pussy willow's fluffy white catkins will bloom and turn green if you add water to the vase. Dried arrangements last forever and many can be changed to suit any season or occasion.