I have a Toshiba Satellite C655D-S5200 and need to install a RAM memory upgrade. How do I do this and what do I use?

Are you confusing memory with hard drive space?

Upgrading by adding more memory isn't going to give you more space to store more music and video games. For that, you need a bigger hard drive.

Almost all games don't require you to have more than 4 gig of memory to play them, and most only require 2 gig.

I just read the specs for you laptop and you have enough memory for what you need. The problem is the overall specs of the laptop, and mainly the CPU.

Here's what they have to say about your CPU:

AMD C-50

The AMD C-50 (codename Ontario) is a dual core processor for small notebooks and netbooks. It offers a relatively powerful integrated graphics card and a single channel DDR3(L)-1066 memory controller. The successor, the C-60 offers the same base clock speed but in addition a short Turbo Core overclocking to 1.33 GHz.

Inside the C-50 two Bobcat cores can access 512KB level 2 cache per core. In comparison to the Atom processors, the Bobcat architecture uses an "out-of-order" execution and is therefore faster at the same clock speed. However, the performance is far worse than similar clocked Penryn (Celeron) or Danube (Athlon II) cores. 

The integrated Radeon HD 6250 graphics card offers 80 shaders and an UVD3 video processor. Compared to the slow GMA 3150 in the Atom processors, the HD6250 offers a lot more performance and is about as fast as the Nvidia ION graphics solution.

The processor speed is somewhere between a single core 1.6 GHz Atom N455and a dual core Atom N550 depending on the benchmark . Therefore, the performance is still in netbook regions and only suited for low demanding tasks.

I wouldn't expect a lot out of the laptop for doing any serious gaming, it's not any good for that. What you have is a laptop that would be good for school work, surfing the internet, some minor gaming, and watching videos.