With plenty of Vaseline or similar coating the joins between the two hemispheres, connect to a vacuum pump and expel the air for several seconds. Turn the valve to ensure the vacuum remains inside and disconnect the vacuum tubing. Screw the handle back on and demonstrate the two cannot be separated.
With a near vacuum formed within, atmospheric pressure is acting on the outside of the spheres, effectively pushing them together. It would take a great force to separate them.
The hemispheres are usually made of brass or similar and are very vulnerable to damage if dropped – small dents can allow air to seep in making the vacuum very hard to maintain.
This demo is commonly used alongside the 'collapsing can' demo which also demonstrates the effects of air pressure.
Simple Magdeburg hemispheres can now be purchased. They consist of two suction cups with handles which can be pushed together to expel the air. They are much easier to use and do not require use of a vacuum pump to work effectively.