The machine-gun synchronisation method was devised by Antony Fokker and first fitted to the Fokker E1 which surprised the British and French pilots at the time. The system was simple - the propellor hub operated a cam which triggered the firing of a round only when the propellor was horizontal during its arc. Apparently it was very reliable, and Vickers pinched it by examining shot-down and captured German aircraft. Prior to that, crude 'deflector plates' were bolted to the inside face of the propellor to deflect bullets - they went anywhere, and I've read that more than once a pilot was killed or injured by deflected bullets. I believe later systems were electrically-operated.
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