How do spacecrafts propel through space where there is no oxygen for combustion?
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Rockets don’t use atmospheric oxygen, they carry all their propellant with them. This is why multiple stages are used, so you can drop the huge propellant tanks it took to get into orbit, and the extremely heavy engines needed to lift those tanks off the ground.
As for what you’re burning, you might be burning liquid oxygen and either kerosene or liquid hydrogen, but these are usually used early in flight, and discarded by the time the spacecraft starts its actual mission(these are relatively difficult to light, and cryogenic propellants don’t keep forever). For the long term propulsion, you usually use hypergolic bipropellants like hydrazine and N2O4, or in some newer satellites, ion drives that use solar power and noble gases.
Monopropellants like hydrogen peroxide are even simpler, but have less shelf life and performance.
How much you can accelerate depends on the mass of your rocket compared to the mass of your propellant, and the exhaust velocity.
If you have single stage a rocket with an exhaust velocity of 3000m/s , that is 90% propellant by mass, you can accelerate by 6.9 kilometers per second before you run out of fuel. This is called Δv (delta v, or change in velocity).
It takes about 9km/s of Δv to get into orbit.
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