Retired NASA manager here, will do my best to keep it 5. There are two methods. Bring your own oxidizer (liquid oxygen) and mix that with something that causes combustion under pressure, usually liquid Hydrogen, but it can also be something simple like Kerosene.
The other is called Hypergolic fuels, and are as reliable as gunpowder. These are two different types of fuels that combust the second they touch. We use helium pressure as an inert gas to push the two together.
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