Believe me, I'm in the process of doing it right now. I've been trying to get my lovely, latest, greatest game to see the light of day for over a year. It should be finished in about a month, after I get my cards cut. I've also done the art for another project, Monkeys on the Moon. (Okay, shameless plug, give me a break. Better yet, preorder your copy now! :-)
There are two big markets for games in the United States: the "Family Game" market, and the "Hobby Game" market. I think the Hobby Game market is easier to get into; hobby gamers are more accepting of small-time operations.
Family Games are usually sold at big outlet stores. In order to get your foot in this door, you'll probably need an agent, and the agent will try to find a big-name publisher to buy it. According to an agent I talked to, this process could take several months. (Funny, designers of this kind of game are considered more "inventors" than "writers", perhaps from the American tradition of having a gimmick in every game. Consider the "Mouse Trap" game, when I say gimmick.)
Then if your agent finds a publisher for you and once the deal is inked, it will take about another year for the game to be printed and for you to see any royalties from it. Yes, the new games on the Toys'R'Us shelf this year, were conceived 2 or more years ago, in all probability. Also, generally big-game companies will not buy from no-name game designers. Generally, co-branded games (games aligned with the next, greatest pop icon or fad) will tend to do well, here.
The Hobby market seems to be a little easier to sneak into with your own cash. If you've got a good graphics program (Quark, Pagemaker, etc.) you could make up your own cards and send it to a publisher (like Carta Mundi), and with a minimum print run of 10,000 decks, have yourself a game. Your decks will probably run you about $1.50 - $2 a pop, so you will have to give them $15k - $20 to do the job. Okay, now you've got 10,000 decks of cards, and you can try to sell them to distributors and such. (By the way, how much space does 10000 decks take up? Better have a spare room handy for storage :-) To be fair, I have seen some places that will do print runs of as small as 2,000.
You could publish the Cheapass way, but even their cards are pretty high quality. You would need some way of cutting the cards evenly, so that means getting your own die-cutter (pretty darn pricey), or having a professional do it for you. Personally, I found a personal die-cutter through a company called Accucut, I had a die (cutting surface) made for my cards, and I use it for the Accucut machine I can rent at a local scrapbooking store. Even having the die, though, it's a time-consuming and sometimes aggravating process.
There's a mailing list on Yahoo Groups called Spit and Bailing Wire which focuses on starting a game business on a shoestring budget that I would strongly recommend joining, if you're into that sort of thing.
Best of luck.