For the beginning curler there is not much else needed in addition to clean shoes for the ice to begin curling. Most clubs will allow you to use their clubs brooms and sliders. The only other thing you will want is some warm loose clothing and possibly a pair of thin, flexible gloves.
As the curler progresses in ability, there are stopwatches for timing the speed of the ice, sliding aids, and outerwear. And even curling sticks for curlers with physical limitations. Sliding aids are used in lieu of the broom during the delivery of the rock for stabilization. This is more a matter of personal preference and technique. A decent sliding aid is around $75 to $100. Curling pants are designed to provide warmth and flexibility at the same time. Jackets tend to be lined nylon. The curling stick is a relatively recent invention that allows curlers with physical limitations such as knee, hip and back problems, to continue to play the game. The stick allows curlers to deliver the rock from an upright position. This creation has extended the career of many avid curlers, and has become so popular that some clubs have leagues strictly devoted to stick curlers.