I wouldn't worry about hurting your hard drive, its very hard to break them unless you drop it, or it gets like a surge of power which it shouldnt when its turned off :P
Ram is easy, just pop it in the slot. Same as video card, 1 screw, maybe a power connector, and pop it in the slot.
Power supply is the most complex part you've got, since you're going to need to completely unplug and remove the old one, and be sure to correctly reconnect the new one. Just make sure if you have a pentium 4 motherboard that you connect the main power connector to it, and the smaller 4 pin one as well. Also be sure to reconnect any PCI cards that may have had power (i know my firewire one does). If you just be careful and take everything slowly you should be just fine.
To ground yourself you just need to touch the metal of the case, but that only works if the case is plugged into the wall still. As long as you're not doing it in socks on a shagg carpet you should be alright
Good luck!