How do I make my mac OS X 10.4.11 faster?

I think need to add memory to my computer, but I do not want it to be external and I do not want to go to the apple store and pay a fortune. I have 512 MB memory, and I want to get around 2 GB. My computer is older and I just want to add some space so it will be faster…

My sister said she bought something at costco or maybe online and was able to do it herself(she was nervous, but she followed some online instructions).

Where do I begin? What do I need to know when looking for this? How do I know it is safe. I would assume I should back up my current hardrive (which I already have with my external hd)...