Coolant leak from a car's cooling system will cause the leak of Orange or Green colored fluorescent water (assuming that coolant is present in the cooling system and not just plain water). Their are at least two colors of coolant as vehicle manufacturers use different kinds. If the leak is large enough, the coolant will form a puddle under the vehicle especially after the vehicle has just been run. Smaller leaks will appear as colored drips on hoses and/or colored drips on parts of the engine. Coolant can leak from any part of the cooling system.
Most cars use a pressurized coolant system to keep the engine at the best operating temperature. This liquid is usually a florescent green or orange in color and freezes at lower temperature than just plain water. The coolant liquid also contains chemicals that prevent damage through corrosion to the parts of the engine and cooling system the liquid flows through.
Before being able to fix a coolant leak, you need to determine the location of the leak. Picture below shows the various parts of the engine cooling system.
Coolant is pressurized (wants to expand in size) as the engine gets warmer. It is like the air in a balloon. The balloon is big to begin with but slowly gets smaller as the air escapes. Any small holes that may not be a problem when the engine is cool become a problem when the engine gets hot due to the pressure increase as the radiator coolant leaks its way through a small hole.
Radiator Coolant Leaks can happen overtime as a Radiator can develop leaks due to rust creating holes and or damage from stones or other items making holes.
Common Radiator Coolant leaks can come from the Radiator Cap. The rubber seal on the cap can break down - Never Ever attempt to remove the cap from a hot or warm system as the pressure could spray you with hot liquid which is a ticket to the emergency room.
Hose clamps can become loose and break. When the clamp is no longer tight it does not form a tight seal on the hose it is around. Radiator Coolant Leaks will occur when the fluid forces itself past the loose or broken clamp.
Rubber and plastic hoses will eventually fall apart causing leak. Metal ones can corrode. Sometimes a hose will look okay but when you squeeze it you will see cracks especially if it is old.
Water pump has moving parts that rely on seals to stop the radiator coolant leaking out and these eventually fail. These seals have to deal with parts rotating against them continually when the engine is running. A water pump can last anywhere from 2 years to 10 years depending on the environment the engine is run in. Sandy environments will wear down the seals quicker.
Bolts may become loose that hold parts tight against a gasket/seal. When the bolts get loose then the Radiator Coolant leaks past the seal or gasket.
The Temperature sensor may fall apart causing a leak. Temperature sensor is inside the pipes for the coolant and if it breaks this gives the coolant a way out.
Cylinder heads may warp allowing coolant to get by a gasket. Other metal components may do the same and cause the same issue. This is a common issue but unfortunately not always a cheap fix.
Coolant is used to supply heat inside the vehicle. The heater core can develop leaks like the radiator.
Gaskets can age and become brittle and no longer perform their job.
Any metal pipe or metal part in the cooling system can corrode over time (develop holes). Eventually coolant will leak out of the corroded piece.