Determine what kind of writer you are. Are you funny? Serious? Or perhaps a combination of both? When writing a TV spec, you want to always play to your strengths. Think about the television shows on the air right now and which ones your sensibilities are most like. Pick your favorite. This is what you should write first.
Read! It seems sort of odd to write by reading. But performing this step now will save you a lot of time down the line. Once you've picked your favorite show, get your hands on scripts of a few different episodes. This can usually be done through an online auction site, a major library (in New York or Los Angeles) or perhaps even by contacting the show itself. However, please note that you cannot sell or copy that material in any way as it is owned by the studio. Reading will not only give you a sense of the formatting but also the structure. How many acts are there? Is there a teaser or a tag? Each network produces shows slightly differently which is why it is best to have copies of the actual episode.
Purchase or download writing software. The predominant writing software in the movie and television industry is Final Draft. While it is an expensive purchase up-front, if you plan on writing it is well worth it over time.
Outline your story. Again, I know you probably want to jump right into writing, but you will save yourself a lot of headaches if you brainstorm and outline your story first. When writing a spec TV script, it has to be completely original and fresh and most importantly feel like it could be an episode that's actually made. This is no small order. Think about the characters of the show you're specing. What completely insane yet totally plausible situation or relationship could you get them into and out of in the length of your script? The more clever the better. Also outline A, B and C stories. If you notice most episodes (especially sit-coms) have 3 stories happening. A major, a minor and usually a third which is a quick brushstroke of a story (usually providing humor or comic relief). Come up with story ideas for all of these.
Write your TV show! Now finally you are ready to dive in. Be sure to keep the same format from the samples you have read. Now emulate (NOT COPY) the way the prose is written, and then in the character voices create dialogue for the show's characters. Think if they always have a favorite saying, or speak a certain way. Remember the whole point in writing a spec is that it could be on the air tomorrow! Refer to your outline often and don't linger in scenes too long. While TV is dialogue heavy because of the fast production pace, they also get to the point of scenes very quickly.
Get notes! This may be somewhat tricky if you are surrounded by people who have never written a teleplay before, but try to find someone (maybe even through an online club) that knows what they're talking about and has written a TV show in a legitimate way before. They will be the most helpful with notes. Listen constructively, don't argue and don't agree with everything they say. Remember ultimately you're the author, so it's up to you. But they are taking the time to sit with you, so give them the respect of listening openly.
Rewrite! This is the thing that most young writers hate to hear. Most people just want things to be done when they get to the last page, but unfortunately "writing is the art of rewriting." Take the notes, think about them, and go about solving how to make your script better. Remember notes are not a math equation. Think about why the person gave you the note and that will lead to your answer. The notes and rewrite process may take a few steps but after which...congratulations! You've written your very first teleplay!