Move to Los Angeles. Right now, there are aspiring writers typing furiously in every coffee shop in LA. To compete in this cut-throat market, you've got to live here like the rest of them. Sending a writing sample and heartfelt letter from Wisconsin won't move you further up the call sheet or stack of scripts.
Write for free. In order to get literary representation (and paid writing jobs), you must often write for free - "on spec" - for years. If you're independently wealthy and can make writing on spec your full-time job, then congratulations! You may get there quicker than some others. Most working writers in Hollywood had "day jobs" when they were starting out, however, which paid the rent. They did their spec writing in their spare time - evenings, weekends, etc.
Have the right samples. If your goal is to be a TV writer, you must have two "spec" scripts for shows that are on the air. These sample scripts must be EXTREMELY current and at least as good as the scripts that are on the air. You must be highly familiar with the show you're writing on spec and watch it weekly.
Have the right samples, part two. Most TV producers insist on reading original material when hiring, in addition to spec episodes of shows on the air. Literary agents will want to read original material, too. So - for example - if you're hoping to work on a broad comedy like "It's Always Sunny in Philadelphia," be prepared to provide an original script, either an original TV pilot or a screenplay that's shockingly dirty and funny.
Be willing to prostrate yourself. Getting your work read is the single hardest part of becoming a writer. This is where your tenacity, tact, humility, follow-through and patience come to play. Since you already live in Los Angeles (see step one), you've no doubt met other entertainment industry professionals. Don't worry if they're young and work in an assistant capacity; it's a largely unspoken secret that assistants run Hollywood. If you can get a literary agent or agent's assistant to agree to read your work, you've rounded first base. Getting them to keep the promise is far trickier.
Keep a level head. I labelled this how-to article "challenging" for a reason. People in Hollywood promise to do all sorts of things they have no intention of doing. Even if they read your script, they might never call you back. You might get signed with a literary manager or agent, only to be ignored for the duration of your time as their client. Most working writers in Hollywood have gone through at least one or two agencies before finding one that works for them and gets them work. No matter how disappointing these set-backs may be, keep writing.