My equipment consisted of a halter, a lead rope, and a stick with a string.
You can also see the lead rope in this picture. It attaches to the halter under the horse's chin, and the person (not shown in this picture) holds the other end.
Your lead rope is kind of like your "hose of communication" with your horse. You might be surprised how much you communicate just by how tightly you hold your rope. Try holding the rope in your hands with your eyes shut and have somebody else hold the other end of the rope -- see how much you can tell about the way they are holding it without opening your eyes!
This is kind of like what a carrot stick and string looks like. It is long (firm but flexible) stick with a string tied to one end. It helps a person (who stands upright) to communicate to a horse (who stand on all fours). It is a very versatile tool. Sometimes it is like a tail. Sometimes it merely gives you a "longer body" (like a horse). Sometimes it is a hoof. On occasion, it acts as teeth. It's basic purpose is to help you talk in horsey language (instead of expecting the horse to understand English).
In reality, I guess this is not a lot of equipment. An experienced person moves smoothly with these things, as though they are a part of her. I, on the other hand, as a beginner, was constantly tripping over, dropping, and tangling myself in these various pieces of equipment. A more "left-brained" horse would have been snickering up her sleeve at my clumsiness. WhiteStar, however, was very patient and nonjudgmental as she waited for me to unwrap myself and get up again. [I am immensely grateful that I did not start out on a wild horse as I imagine what would have happened if the horse had spooked while I was tangled. Yikes.]
When I rode her, I connected both ends of a rope to her halter to act as "reins". Occasionally, I put a bareback pad on her, but she is so comfortable to ride that I usually rode completely bareback. Riding bareback is fun. It definitely makes me feel connected to my horse, and it also helps me pretend that I am either an Indian or some girl taming a horse in the wilderness. :) It is very "natural" and I like it.
So that is the equipment that I used on a regular basis to work with her. In addition to that equipment, I learned to used various kinds of brushes, a hoof pick, and special non-chemical fly spray.