More information is needed to adress your concern.
Type and year of the vehicle, engine/fuel type. Is it fuel injected?
Does the engine spin over?
Fast or slowly?
Do you have spark?
Does it have an immobilizer or an alarm system that affects spark and /or fuel (anti theft device)?
In order for an engine to start, basic criteria need to be met.
What needs to happen:
Proper air fuel ratio.
Compression of the air/fuel mixture.
Ignition of the air fuel mixture at the proper time and suficient voltage.
You must have sufficient compression.
The engine needs to be spun at a fast enough speed to develop the compression of the air fuel mixture. (The battery must have sufficient charge, the starter must be functional and the engine must be mechanically able to develop the compression.
You must have fuel. (proper fuel air ratio)
The fuel must be injected in the proper amount at the proper time, on fuel injected vehicles (air fuel mixture atomized properly on carburated cars).Fuel pump, fuel filters, fuel lines, fuel injectors (carburator),or electrical problems such as loose wire connections broken wires or faulty electric control units could be a problem.
You must have spark.
The spark must be delivered to the proper cylinder at the proper time at a voltage level sufficient to ignite the compressed air / fuel mixture.
The ECU controls spark based on engine sensor inputs on newer vehicles. Older vehicles a distributor (distributor cap, distributor rotor, ignition coil & plug wires as well as spark plugs could fail). Electrical problems including a weak battery could affect the spark level.
The engine must be properly timed for the above to take place.
(timing belt / timing chain or gears to ensure crankshaft camshaft timing).
Anti theft devices such as immobilizers or car alarm systems can also cause no start conditions, they may interupt the voltage supply to the starter, fuel and ignition systems.
Hope this information helps.