Size and construction varies depending on its uses. They can vary from 35 feet to 70 feet with walls being at least six feet tall and the footing should be right at four inches deep.
The size and type depends upon what you plan to do. Heres some examples:
~Pleasure Riding 100 X 200
~Dressage 66 X 198(or 132)
~Barrel Racing 100 X 260
~Jumping 150 X 200
There are of course other sizes I've not listed and they too depend upon your type of riding.
The fence should be at least 6 feet tall to discourage horses from putting there heads over the rail as well as helping to prevent distractions. Strong fences are an assett. The shape depends on your type of riding also. Rectangles allow you to ride your horses deep into the corners to teach them to bend. Oval arenas (or rectangles with rounded edges) are more convient for jumping and driving. They are also easier to harrow. Gates need to be flush on the inside with the latch operable from horseback.
The arena should be on dry well draining ground with a small ditch dug around the outside of it if needed. The site should be level with either the center crowned or gradually sloping 1-2 degrees from one side to the other for drainage to avoid puddles. A steep grade could lead to erosion of the surfase soil during downpours.
Footing must also be weel good coushined(see more on surface material below). The type depends upon your climate, type of activity and if it is indoors or outdoors. Some examples are: pleasure, jumpers and dressage horses work well with firm footing without excessive depth of some coushioning as sand or sawdust; game type events(barrels, reining etc) do best on a firm base(see more on base below) with a slightly slick top of sand.
Mixing sand and/or sawdust in with your native dirt will lighten and loosen the soil and increase its drainage while adding to its cushion. Add stone dust a little at a time if you are trying to firm up the footing. There are also processed footings available you can spread over a firm base but some of these are best used in an indoor arena.
Good footing is safe and can encourage a horse to move forward with energy and elasticity. Poor footing is dangerous and can cause a horse to move timidly or with resistance.
The layer of material between the "earth" and the surface material is called the base. It's functions is to act as a protective layer between the earth and surface materials, providing stability to arena floor and carrying rainwater off the arena. It could be naturally occuring material or added material with a rock base or fine gravel topped with stone dust and clay. This base should be packed or tamped as hard as concrete. The base should be thick enough to prevent "earth" from working up through the base into the surface soil. The thickness varies depending on what is done on it and the area. 4 - 10 inches is common.
This is the "cushion". Often it's a mixture of materials and depending on the base and the arenas use the layer should be between 2 - 6 inches deep. The mixtures vary. Some examples are sand, silt, clay, topsoil, small pebbles and various artificial footings.