Purpose: use corners better, lighten shoulder, prepare for next movement. For dressage riders, jumpers, or anyone wanting their horse to lift her shoulder at the half halt.
Set up: three cones per corner, approximately 1m off wall (more or less depending on your level). If you do not have a square ring (I have rounded corners), set up fake corners using poles - so a small square within your circle/oval. My trainer had this set up for me today to work on using my corners better. The reason to do this isn't just to take advantage of the space, but it sets up the horse for the next movement. If you need to do a serpentine, half pass, shoulder in, or just go down the long side with a bit of bend, this will help you make the corner depth correctly.
Methods: Trot or canter a 20m circle inside the cones at one end, then walk at the first cone, prepare at the second, and trot or canter at the third. Do a 3 or 4 loop serpentine or other exercise between ends or alternate between circle (inside) and using corners (outside). Mix it up and sometimes do not walk. You'll find your horse picks up the inside shoulder and half halts automatically after a couple of attempts.