Using anti-static wrist strap to ground against laptop

The purpose of grounding is to allow electrons on you to flow to an object so that the voltage difference between two objects is 0. This is so you don't dissipate the voltage directly onto the motherboard and other vital components.

Mike Insch does not understand the concept of ground. A ground is merely a reference point for which other objects voltages are compared to. The electrical earth might actually have a different electrical potential from that of the chassis. This could very well be the case in laptops with only two prong power supplies

A laptop chassis can be a ground, as long as it is on a good conductor. Those plastic chassis won't work. Also, it is really difficult to find an appropriate place to clamp the wrist strap. Also, I have had many laptops power supplies only have TWO PRONGS. There is no connection to the electrical earth.

The laptop should not be worked on while plugged in or with the battery in not because of lack of earthing, but rather because there is current still flowing through the motherboard.

You do not want to ground yourself to the laptop. You want to be grounded to earth.

The anti-static wrist strap should have come with an attached wire. The other end of that wire should be connected to an electrical ground. The center screw of the AC wall outlet holding the cover plate is a suitable connection point that is tied to your dwelling's ground (assuming you have 3-prong outlets and the outlet is properly wired and up to code). Make sure you attach to bare metal and not the paint on the screw.

Once you are grounded, you do not want to touch any live circuit. So the equipment should be turned off and unplugged. Ideally, especially with high voltage devices, you should use the hand that has the strap to poke around and the other hand behind your back or in your pocket. The idea is that if you do get shocked, the electrical current only has a path from your hand to the strap, and not across your chest and heart.