first things first, all kinds of things can go wrong when adding RAM sticks. the best approach would be to look at all your specs with software tools like SIW .
If you use the proper module/s you shouldn't have any problems. SIW is a nice application for finding system information, but to find out exactly what you have for RAM you should use a program like CPU-Z. Better still, just go to a RAM manufacturer's website to find out what RAM is compatible with the computer, example: Crucial suggest that this computer uses DDR2 PC2-5300 and has a maximum of 2GB of RAM.
I would NOT recommend buying the RAM online unless you use newegg
Newegg is a very reputable online company, but there are companies like Crucial which can match and guarantee the modules will work with the computer that it is intended for.
get some latex gloves on your hands
I worked in an industry where we dealt with ESDs on a daily basis, I was tethered to a ground via a wrist strap, wore clothing which was designed not to create static electricity, even wore ankle staps... but latex gloves ain't part of the program. Most ESD problems can be resolved by discharging your body prior to touching anything inside the case, this can be done by touching anything metal close at hand.
dive into your BIOS to check for RAM installation variables
In almost all cases you shouldn't need to fool with the BIOS if you are using modules which are proper for the application and all have the same voltages.
Hope this helped.