Cultivate a source on the inside. The best way to submit a pilot to FX would be to have someone you know push it with FX coworkers. This sounds basic, but it's the way things work in the television business. This person on the inside doesn't have to be high up in the chain, either--it can be someone who works for FX Networks and who can get the "right ear" when it comes to the pilot. You might also apply to work in the FOX Forward Internships Program, where you'll gain access to some of the highest-level people within the network, while also gaining valuable experience.
Use social networking to get noticed. If you subscribe to FX Networks on both Twitter and Facebook and post regularly, you might attract someone's attention at the network. (This is what happened with CBS and the man who tweeted "S*** My Dad Says" on Twitter--which has now been picked up as a television series.) Make sure your postings are clever, creative and show off your talent to the highest degree. If you're tweeting about what you had for lunch, the odds are that you're not going to attract any kind of attention.
Call FX Networks and ask to speak with someone in the programming department. You'll be sent to a low-level individual, but if you have a telephone pitch that is sufficiently intriguing, you might be passed up the chain of command to someone who is able to request your pilot. Before making that call, make sure your pitch is as perfect as you can make it. You'll want it to flow easily and naturally, giving out enough information to make your premise known but without giving away every plot detail.
Contact an agent specializing in television pilots. You can find them on websites like Writer's Market and Literary Agent Marketplace. If someone at FX requests to see your pilot, they are going to want to deal with an agent. This is because television is a very expensive and serious business, and it's easier to deal with agents who understand how things are done rather than with a "civilian" who might insist on rocking the boat.