I used to have economy 7, and don't know if there is any difference.
You don't do any switching on or off, it is automatic. The timings vary a little from region to region so there isn't a mass switch on that would overwhelm the Grid.
When the clock switches on your storage radiators start heating and store the heat in bricks.
Your hot water tank has two elements. The economy 7 one is at the bottom, and as hot water rises it heats the entire tank. A second element at the top runs on full price electricity, and kicks in during the day if you use up all the hot water. You can always turn down the setting on this second element so it doesn't use much electricity, if for example you live alone and don't need it reheated after your evening bath.
Some washing machines incorporate delayed star ttimers, so you can set it to start at perhaps 5am in the cheaper period. When you wake your washing load is ready, and your neighbours in the downstairs flat scowl at you because of the noise.