Above we discussed keeping your components safe, but there are a couple of things you need to do to keep yourself safe. It may seem a little bit condescending to have to spell it out, but people have done crazier things out of blind ignorance.
Safety Rule 1: Unplug the laptop. I shouldn't have to tell you that if you touch the inside of the laptop while it is plugged in there is a really good chance you'll end up electrocuting yourself - especially if you're also handling a screwdriver. It might not hurt you, but your likely to fry you gear. Even if, technically, the components shouldn't be receiving power because the laptop is (hopefully) not powered on, why risk it?
Safety Rule 2: Remove the Battery. Again, electricity running through components that you are poking with a screwdriver isn't a good combo. The battery probably won't transmit power if the laptop is off, but you don't want to find out first hand that it isn't working as intended. The point of a battery is to hold a charge, and unless you're an electrician or electrical engineer there is nothing you can fix in there, so never mess with the inside of a battery.
IMPORTANT NOTE ON WARRANTIES: As a last warning, disassembling your laptop - even if it's just a little bit - will void your warranty, assuming you still have one. It doesn't matter if you know what you are doing or not - if you are not a certified technician documented with that company, you are not allowed to work on a warrantied machine. Will they ever find out that you have? Probably only if you screwed it up. There is a rumor that there are hidden "seals" inside laptops that will break and let "them" know you broke the rules. That's an urban legend. Technicians are barely trained, and determining if something has been tampered with is the last thing you'd ever find in a training manual. (Then again, it's pretty easy to put a sticker on the inside of the laptop where it will be damaged by disassembly, and the first, possibly only, thing an OEM technician is trained to do, is find a reason not to honour the warranty -Ed). Regardless, disassemble at your own risk. If you mess up and get caught, you can't say I didn't warn you.