Submit it to the major search engines. Most of your traffic should come from the big 3 - google, yahoo and bing
You can submit your website to some main SE such as google,yahoo and etc...Try to learn some knowledge on SEO.PPC is also a good way for your promotion.Maybe you can have a try.
You can go over to www.talkarcades.com lots of knowledgeable people over there. But as a ncie easy tip, banner exchanges are a good place to start. www.funklicks.com www.mibbi.com www.moreplayerz.com Loads out there.
Try going to adbrite. com. There you can find websites that get a lot of traffic and are geared towards gamers. You place your own banners on the sites you pick. Also you can choose to pay for CPC or CPM. I suggest the CPM. you also get to name your own price.
If you are looking for immediate traffic, write an interesting press release about games and your website and publish it to ate least 10 press / article websites. Then submit those pages to the most popular social bookmarking sites like stumbleupon, digg, delicous, yahoo buzz and reddit. You will see a great incerase, but do not forget that if you want a steady traffic you must do some SEO work and prepare good valuable content. If you wish to pay for advertising, look for websites that are similar to yours and ask their webmasters for links or blogposts, that could be the cheapest advertising for a gme related website.