Q: Hello, I'm replacing my computer's Power Supply, and I need to know how to be grounded when I am. I can't use the PSU itself to ground myself since I won't plug it in until I'm done replacing it.
A: I can't blame you, there are plenty of reasons when static charge is high like low/no humidity, combined with a shag carpet, it's just asking for trouble. If there are other devices around you that have a metal chassis you can ground out there, or even directly to the earth ground on three-prong outlets or the outlet cover if you are not comfortable plugging in your wrist-strap into an outlet or power cord :), that's about as direct to earth ground as you can get. If you are stuck on a carpet with no ground strap, I would wear shoes, discharge w/ bare hand to something metal nearby (preferrably a metal chassis device plugged into the wall) and not move feet at all when handling components. If you have to move put the component down, move around as needed, then re-ground to discharge any static build up. Most shops that have a carpeted build / maintenance area should use a large static mat with similar earth grounding.