If your computer case is metal, just rest your forearms on it while you're doing the work. (Make sure to touch arms to case before touching the insides of the computer or the part.)
And, as I believe Leau said, you can always buy a mat at a computer store. They keep the computer grounded and should come with a wire and something to attach the wire to your arm - this will keep you and the computer both grounded and the mats usually prevent static electricity.
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"Without the darkness, how would we see the light?" ~ Tuvok
Editor for Television Category