Practice on an old radio first.
Let the tip of the iron heat up sufficiently before doing anything.
Don't over do it. apply just enough heat to what you want to solder to melt solder, then back off. Apply the very tip of the iron to the spot where the component passes through the motherboard. There should be solder already there, so the instant it starts to melt, touch your new (very thin) solder wire to that exact spot (it should immediately melt) then pull away quickly.
DO already have the computer unplugged from the wall, and DO unplug the power supply from the motherboard.
Uh Oh. This is a lap top isn't it?
Back up.
Gather many chickens, get some garlic, and wolfbane. Get an old dried out goard, and paint celtic runes of digital empowerment on it. Get a badger skull and eagle feathers and make a high priest's head dress out of them. Face Stonehenge, and offer the chickens up for sacrifice. De-feather the chickens, wash them, make some batter, heat some oil, then fry them babies up. (call me when they're ready) Have a gallon of sweet tea handy, too. :)