Just like a conventional piston engine with poppet valves (Otto cycle), Wankel engines operate on the four-stroke cycle (suck-squeeze-bang-blow).
This Wikimedia animation succinctly describes it:
The rotor seals off the air/fuel intake charge from the intake port, gradually compressing it until it is sufficiently compressed, at which point the spark plug ignites the mixtures, generating rotary motion which then carries the combustion gases towards the exhaust port and out.
Some noteworthy characteristics:
look mom, no valves!
which means no need for cams, camshafts, timing belts, etc.
smooth power delivery
due to the absence of reciprocating motion that is inherent to piston-engines.
oil needed for lubrication
the oil is needed to lubricate the rotor and is mixed with the air/fuel intake charge, so the engine will by design consume oil at a faster rate than a well-designed piston engine.