Most of the time you have to know who to know... Use your time at Gen Con to attend game publishing seminars and such. There you will get the chance to meet some industry insiders as well as some publishers.
Publishers are always getting pitched game ideas. Most don't want prototypes, they want completed games that are ready to sell. Some only want a specific type of game, and some only want to hear from established developers. Breaking into the game industry is not an easy task for new developers and it is not uncommon for people to be ignored when pitching their game. Publishers are in the business of getting the game on the shelves of stores. A busy publisher doesn't have time to do the work of developing the game as well as publishing it. Developers are the ones who write, test, design, layout games.
I would recommend going a self publishing route for your first game. Get a few copies out to some reviewers and other industry insiders and give them time to playtest it. Be prepared for the harsh (or good) criticism and build on it. Once you have a game out there, you will find publishers more apt to hear your next pitch.
For TCG, you should contact a local printer (companies like The Ink Basket also do this kind of work) and have a demo professionally made, or you can go through a company like Gamecrafter.com or Makeplayingcards.com where it may turn out to be more expensive unless you are prepared to order in bulk and getting your finished product may take longer to receive.