Good points in this thread so far.
I work with ESD destroyable devices every day. In the absence of an anti-static strap, here are a couple of ways to keep from frying things:
1. Do the work on the kitchen table or counter. If you have linoleum, tile, or hardwood floors, take off your socks, and touch your water taps before working on the machine.
2. As mentioned, it's best to leave the power supply plugged in to the wall, as long as it has an off switch. This keeps the case grounded. But make sure the power is off to the motherboard before removing any components.
3. Don't wear any synthetic clothing while you work on the machine. Denim, cotton, etc., are all fine. Removing the socks will help you not build up as much of a charge as you move around on the floor.
Finally, an important safety tip. Never
try to make a home made ground strap out of your metal banded wrist-strap on your watch without some sort of resistance in the wire lead. Say 1 to 5 MegOhms. Hooking a wire from your metal watchband to an Earth ground without resistance is just asking for an electrocution accident. It can happen quite easily if you're grounded this way, and it's dangerous.
So, for anyone wanting to work on their machines, and they feel they really need to use a strap and want to make one, you can pick up temporary ones for $5 to $10 that will last a long time for occasional computer work. This is a much better idea all around. Please do it that way if you must use a strap. I want to read what you post, not read about why you can't post anymore.