There is no one method that can satisfy all requirements and situations in vacuum systems. Leak detection is no exception. There are four main methods used: the bubble test, pressure drop test, pressure rise test, and helium aspiration mode/helium vacuum mode tests.
These four tests correspond roughly to the "simplistic", bubble test or bubble emission test (for low vacuum pressures), and the "high tech", helium tests for high vacuum pressures.
You can demonstrate the bubble test by either placing a perforated bike tube under water and marking the source of bubbles, or placing a dishwasher at the joint between a gas and active water pipe to see if liquid foams.
Both methods are reliable in detecting low pressure leaks. The bubble test can be used for vacuums up to 10-4 mbar.
Pumping is done by vacuuming a container that is sealed until it reaches a certain pressure. Then, the inlet valve is closed.
After a predetermined time, the inlet valve closes again. The time it takes for the vacuum pump to return to the original evacuation level will be recorded.
This is repeated many times. If the time it takes to return the vacuum back to its original level is constant, it's a sign that there's a leak. This indicates that there is a decrease in the gas release from the system (i.e. a "virtual leak"), but it does not necessarily exclude the possibility of a leak.
Alternatively, you can perform the pressure rise test by plotting the vacuum against time after a vacuum has been reached. After isolating and inspecting the system, the curve should be straight if there is any leak. If the pressure rise is due to gas released from the system walls, it will slowly decrease until it reaches a stable value.