The clutch system in our cars is hydraulic, as apposed to a mechanical system, and uses brake fluid. There is a clutch master cylinder and a clutch slave cylinder. The master cylinder is bolted on the firewall next to the brake master cylinder and attaches to the end of your clutch pedal. When you push in the clutch, the pedal assembly moves the master cylinder rod in which pushes fluid through the brake lines and to the slave cylinder. The slave cylinder is mounted on the transmission. The rod on the slave cylinder pushes the clutch fork.
Brake fluid is added through the clutch fluid reservoir. DSMs can use DOT3, DOT4 or DOT5.1 brake fluid, but only one type. You can not mix different types of fluid.