Troubleshooting can seem like a mysterious “black art” practiced only by professional mechanics, when you don't know enough about how certain systems in your car work. Figuring it out is simply the result of having the right knowledge combined with an intelligent, systematic approach to the problem. If you work by a process of elimination, starting with the most likely cause and working through to the more complex, you can quite easily yourself diagnose the problem.
There are several different ways that the clutch on a manual transmission equipped car can go wrong, but it is a simple mechanical system, or hydraulic/mechanical, and not hard to understand. Once you understand the parts, and how they interact, finding and fixing the problem should be easy. There are two basic ways a clutch fails - it either fails to disengage, or fails to engage fully.
In normal, modern stop-and-go driving, you probably press the clutch pedal in every few seconds. And on that one time when you press it and the car still creeps forward, you know you have a problem. Sometimes a part fails and the clutch goes from working normally, to not working in an instant. Other times it is a slow gradual change, with each use of the clutch working less and less well. Each of these failure modes has different causes, and how it failed can be a big help in figuring out how to fix it.
A clutch that doesn't engage fully, or slips under heavy load, is the normal failure mode of a worn out friction disc of pressure plate that has lost its tension. When you press the clutch, your foot counters the diaphragm spring which presses the friction disc to the flywheel. If the spring pressure is not great enough, or the clearance between all the parts is too great, there won't be enough friction to transmit the power from the motor to the transmission. Friction discs wear and get thinner, and springs get weaker with time and use, which is why all clutches eventually start to slip. The sudden onset of a slipping clutch usually indicates that an oil leak, or something else has contaminated the friction surfaces.
Clutch does not engage at all
Clutch slips under load
Beside not engaging, or not disengaging, there can be other issues as well, such as noisy operation, or chattering on engagement. On older mechanical linkages, lack of periodic lubrication can lead to high effort or binding in pivots or cables, or a pedal that does not return smoothly. A bad throwout bearing can be a major headache in stop and go traffic, making horrible noises every time the clutch pedal is depressed. These are often annoyances more than anything else, especially since fixing them often involves removing the transmission/transaxle to get to the parts.
Squeal or rumble when pedal pressed
Rattle or clicking from clutch
High pedal effort
Clutch pedal fails to return