You'll have to open your case and look for the board's manufacturer and model printed on the board itself. Then visit the support pages for the board on the manufacturers website. There is usually a 'CPU compatibility' section which will list all the CPU's your board can use along with the bios required.
Your own bios version will be displayed at startup (briefly), or you can usually go into the bios (press 'delete' at startup) and find it at the top of the screen.Only update the bios if you have to.
Incidentally, upgrading the CPU may only have a marginal effect on games - a faster graphics card may have much more effect. 4Gb RAM is plenty, but need to watch that our power supply is up to a bigger card. What graphics card are you using at present?