First, each component is checked by itself, then the different systems undergo operational and functional tests on ground. Certain avionics equipment will also have it's calibrations checked.
These are part of the regular work package, plus those tests as per AMM, which refer to components which have been found faulty during the check and accordingly been replaced.
When all ground tests have been finished successfully, the plane will after a heavy check be taken up by a test flight crew under a permit to fly for a test flight, where the systems are being checked again under flying conditions, e.g. the plane will do a autoland in good weather to check if the system works, or the plane will be intentionally depressurised above 14,000 ft to see if the oxygen masks deploy. The RAT will be deployed and usually such a flight ends with a gravity extension of the landing gear.
All ground tests will have been certified for by the respective mechanic or inspector who performed them (in Europe the JAR 66 B1 or B2
licenced AME), in some cases additionally by an inspector who did a duplicate inspection.
After the plane has been put back into flying condition after the flight test (e.g. RAT and oxygen masks stowed and all snags rectified), an inspector (in Europe a JAR66 C licenced AME) will sign the final release to service. From then on the plane is good for revenue operation.