Don't listen to them about grounding yourself or touching the top of the case. Listen to me instead.
Touch the metal part of the case (the top might be plastic). You don't need to worry about where your feet are, just make sure part of you is in contact with the metal portion (interior) of the case at all times while installing the card to ensure that you don't zap your motherboard.
Also, if your agp slot has one of those little white snaps on the right hand side, make sure you push that all the way down to release your card before yanking it out. Plus, be sure when you put in your new card that you use enough force to get that little white snap to click into place.
Be prepared for your graphics to look like ass when your computer first boots up with the new video card. If you get a picture at all on boot the it's probably working properly. Have your new drivers handy for the install of the new card.
All you need to do is make sure you know the name of your old card so that you can download the drivers if you need to put it back in for some reason.
I find that the easiest way to remove the old card without grabbing on to all of the circuitry is to (as you're facing the open side of the computer), from the outside of the case, poke the flat part of the metal portion of the video card toward you with a screwdirver. That will dislodge it from the AGP slot (as long as you already have the white snap depressed), then you can grab that same metal part with your hand to remove it the rest of the way.
Don't be afraid to use a little elbow grease and remember that the circuitry is actually fairly resilient (as long as you don't poke at it with the screwdiver or snap of capacitors). Try to touch the video card on the sides only if possible.