A dummy board has two main uses. When inspecting a full hive, it can be withdrawn before any frames of wax comb are removed. This gives space in which to work within the hive as sometimes bees produce uneven comb that cannot easily be removed without crushing bees so taking out the 'board allows for the next frame to come out without crushing bees. The result of using a dummy board is that you do lose a frame in the hive so a National that can accommodate 12 frames can house 11 frames plus the dummy board. The WBC hive is one less.
The other use of a dummy board is when you have a new and small colony of bees so you can control the space they occupy. Bees need to keep their brood warm and a big box will naturally need more heat and slow brood build-up. Therefore a dummy board can be used to restrict the bees’ space. When placing the bees in the hive, rather than put them in the middle, they can be put at one side with just one or two frames of foundation extra. Then the dummy board is inserted. Then 'spare' frames of foundation after that – outside of the area controlled by the dummy board. As the foundation is drawn, and the bees increase their brood area, the dummy board can be moved until it is on the outside of the hive. I’m not convinced that a dummy board makes a huge difference to temperature regulation as heat will rise over the top and go around the dummy board. It’s up to you if you use one for this purpose.
With a dummy board there will be additional space in the hive as the dummy board is usually thinner than the 35 mm of a standard frame. What do you do with the extra space? The answer is always to push the frames together firmly after an inspection so the self-spacing Hoffman parts of the frame meet; otherwise you will find that the spacing increases over time as the bees propolise the hoffman parts. The space will be on the outside of the dummy board – between the board and the side of the hive.
Dummy boards can be made quite easily with offcuts of wood. They are often 12 or 18 mm thick depending on what you have available. If you have a small colony in a full-sized hive, the dummy board can be >100 mm wide (and insulated) so as to use up the space the bees don't need. Don't use dummy boards that are made from frames with a thin piece of plywood in the place of foundation. Bees will draw out the comb on the side of the frame of beeswax next the thin plywood sheet so that a full frame will not fit when the dummy board is removed.
Come winter, you can use two dummy boards, one at each side of the hive. if these are now pushed up against the side-walls of the hive (and not the frames) they will increase the hive wall thickness and thus add a degree of insulation. Not this is not going to make much difference if you have polystyrene hives as they are already well insulated.
Some people don't use them, some people do. See how you get on with one and decide yourself.