|-Make sure to disconnect the power cord.|
Then you remove the earth path and there is nowhere for static to go.
-Put the tower on top of cardboard box(to prevent further build up of static energy)
Pointless: Static within the computer is continually being drained to earth while the computer is operating, It is static build-up in the body that is the problem. A cardboard box inst going to you much good if you are wearing nylon underwear and walking on a carpet made from artificial fibre and the humidity is low and your house has a faulty earth in the power supply, all of which can increase the possibility of static build up.
-Connect it to the wrist and alligator grip to the system tower & u are done
So you and the case of the same potential except the components which are isolated from the earth potential, Touch them and any difference is transmitted to them and zap!!!. The idea is that any static in your body is drained to earth so that both you, the case and the components all at the same potential.
Having said that, I have never used a wrist strap. Just touching the case with the power supply plugged in has all that has been necessary. But people are different, some people can attract static like flies to a pot of jam in which case an anti-static strap is essential.