Starting a jet engine is nothing like starting a car, and just starting one is considered the most stressful part of its entire life. The heat produced during engine start at the inlet to the turbines shoots up to the highest Turbine Inlet Temperature at any point of engine operation, which is why the process is so carefully controlled.
The main challenge with starting a turbine engine is ensuring there is sufficient airflow before introducing fuel. If the compressor blades are not pushing enough air through the engine, introducing fuel and beginning combustion will cause the engine to overheat and damage it. This is called a hot start.
The start function involves turning the shaft that the compressor is mounted on up to a rotational speed of approximately 41 to 62 percent of maximum RPM. On most large commercial jets, this is achieved using the Auxiliary Power Unit, a separate small turbine engine located in the aircraft's tail that produces bleed air from its high-pressure compressor. This air is used to spin the turbine blades of the main engine. If the APU is not working on the ground, a start cart can be brought to the aircraft; it is literally an APU in a wheeled cart, and start carts are at every major airport.
Once the shaft reaches the correct RPM, the Fuel Control Unit begins to introduce fuel into the combustion chamber where high energy igniters light it off. The starter remains engaged and continues to assist the rotating shaft until the engine reaches ground idle, usually around 70 percent N1, where it becomes self-sustaining. On smaller engines this process can last approximately 15 to 25 seconds, but on large high bypass fans it can take 40 to 45 seconds or more.
Once one engine is running, its bleed air can be used to start the remaining engines through a process called cross-bleed, avoiding the need for the APU entirely.