Ok, here's what I would do. I hate those anit-static wrist straps and such and will never wear one. They get into the way and annoying.
ALWAYS have one hand or arm touching the metal chassis of the case. I know it can be hard to do this especially when you're handling parts, but you'll know soon enough once you can figure out a comfortable position. I usually touch the case first to get rid of the static buildup. Then immediately handle the parts carefully on the edges, NEVER on the surface where all the IC's, bus, etc are. Insert it and repeat the procedure again. If you work high on a worktable, this will be easier. My arms are always touching the case when I have the parts in my hand.
Insert components evenly on both sides and push down gently. Make sure everything's lined up correctly before doing this. Secure. My instructor taught me that one hand rule by the way and I always got in the habit of doing it. As long as you are grounded in some way, you should be safe. There are anti-static mats, wrist straps you can get, but not necessary if you know what you are doing.
