I would be hooked to it via a wrist strap.
Ah, good. The most important thing is for you and the equipment you are working on to be held at nominally the same potential, rather than necessarily being at actual ground potential. The additional benefit of having a true ground (earth potential) reference is that it is a known quantity - otherwise with static electricity the potential of anything is unknown until you encounter it.
The requirement for anti-static protection is the same for both your personal anti-static strap connection, and any further earthing strap. With any equipment that doesn't have an obvious metal plane to ground, such as a laptop, for either to be most effective you need the connection to go to something metal that is connected to the ground plane of the motherboard. For a desktop computer, this is assumed to be the metal casing, or if the box is plastic, the metal casing of the PSU. On a laptop, something that carries a ground connection for the purpose of shielding (not signal) is suitable, eg on my HP I would clip onto the threaded securing pin on the dock expansion port.
Edited by Platypus, 16 March 2012 - 08:24 PM.