Q:

Grounding Yourself When Working On Electronics

I was wanting to discuss if using a wrist strap connected to a in unpainted screw on a pc power supply (this screw is a mounting screw it is not touching anything inside the power supply) that is not connected or mounted to a computer as a grounding device to avoid static electricity damaging components.
Of course the power would be switched off but it would be connected to the outlet.
Would this be an effective grounding procedure?
Would this still cause static electricity to transfer since electrons transfer to what electronic you are working on since the power supply is not connected it it (like for instance a pc)?

A:

In addition to the other comments/replies, I'll add that an ESD wristband, by itself, doesn't provide much benefit if your goal is to prevent electrical overstress (EOS) due to electrostatic discharge (ESD). You also require a work surface made of engineered, static-dissipative material that is electrically bonded to the same ground as your ESD wristband. 

:: IMPORTANT ::
Your work surface should never be a conductive material (e.g., metal) nor an insulating material (e.g., plastic laminate); it should only be a properly grounded, static-dissipative material.
Imagine handling a circuit card that has static charge on it and laying that card onto a metallic surface.  The instant the card contacts the metal surface there will be a rapid transfer of charge (ESD) between the work piece and the work surface. This rapid transfer of charge (think short duration, high current) can easily cause electrical overstress that destroys sensitive electronic components on the card.
Now imagine using a work surface that's covered with material like plastic laminate that is acts as an electrical insulator.  You place an item (e.g., your smartphone) onto the surface, and static charge is transferred from the item onto the surface. If you now remove the item from the surface, you now have an island of static charge on that work surface. If you now deposit your circuit card onto (or even nearby) that statically-charged island, the electrostatic field can damage sensitive components on the card if the island's electric field strength is large enough.

So in addition to wearing an ESD wristband you also need to use a static dissipative work surface that is electrically bonded to the same ground as your ESD wristband, and you need ESD-safe hand tools.
Bottom line, you want to ensure

controlled (i.e., low current) transfer of electric charge between you, the work surface, and the work piece, and
that you, your hand tools, the work piece, and the work surface are all roughly the same electrostatic potential.

If you frequently work with exposed electronic components/circuits, there are some relatively inexpensive ESD mat kits you can buy.  Try an Internet search using the keywords "esd field service kit" or "esd mat kit" or similar.  Other useful Internet searches would be "managing esd" and "managing electrical overstress".
(NB: When working with electronic components/assemblies that are sensitive to EOS, never lay those items onto the outside surface of an anti-static bag or static shielding bag. The bag's interior surface/layer is engineered to have static-dissipative properties, but the bag's outer/exterior layer might not be static-dissipative. Furthermore, with static shielding bags, sharp wires on a circuit board can puncture the bag's outer plastic layer and make electrical contact with the bag's matallic-coated intermediate layer(s), thereby shorting together circuit board nodes that should not be shorted together.)

