My computer came with 4 GB of ram, so if I install another 4 GB of ram will it make games run faster?
If your operating system is 64 bit as opposed to 32 bit, it's likely that adding another 4 GB will improve performance. Some older machines will not upgrade beyond 4 GB, so you'd want to check on that aspect of your computer.
If your operating system is Windows, you should see an improvement. If you are using a desktop computer and it is configured for integrated graphics, you can also get a better gaming result by adding a dedicated graphics adapter, with as much on-board memory as you can afford. This will reduce some of the processor workload, making even more use of the additional 4 GB RAM.