How do big planes like 737 manage fresh air for passengers during flight?
They bleed hot compressed air from inside the jet engines, cool it down and pass it into the cabin. There are outlet valves in the fuselage that allow stale air out and which control cabin pressure and air-refresh rates.

A few aircraft types, such as the 787, now use a compressor to take in air from under the aircraft. They do this because it can be more fuel-efficient (not for any other reason). It is arguable whether it creates an additional fire hazard.

See also 


Why is the compressed air (from Engine Compressors) taken from High Pressure (HP) stage instead of Low Pressure (LP) stage
Can an aircraft re-pressurize at high altitude?
Is constant air pressure maintained inside the fuselage?