Odds of Getting In
Unfortunately, TV writing is crazy competitive and the success rate is rather low. Most aspiring TV writers spend their first ten years as assistants, just trying to break in. Also, there's no singular path to becoming a TV writer, which is why this career requires a ton of patience.
Some writers are lucky enough to make a hit web series, score an agent, and get staffed overnight on the next big sitcom—but those success stories are one in a million.
Most aspiring TV writers start at the bottom, hoping to slowly work their way up. This means initially getting a job as a writers' room PA or production assistant. As a PA, your tasks will include fetching coffee, picking up smelly lunches in your car, and getting yelled at by pretty much everyone.
If you're lucky and the show you're on gets a second season, you may get promoted to showrunner's assistant. Alternatively, you could score a gig as a writers' assistant, which basically means you get to act as the court reporter for the writers' room. These are both highly coveted positions because they're so close to the action. The downside? You're still just an assistant.
Many aspiring writers end up floundering for years because shows get canceled, and if a show gets canceled, that potential promotion also goes down the drain and you're forced to start over at the next gig.
An ideal scenario is to get promoted to writers' assistant or showrunner's assistant, to script coordinator (which is basically just a glorified writers' assistant), to the holy grail, staff writer. But making it through all of these rungs is nearly impossible, unless you're lucky enough to end up on a hit show with multiple seasons and a generous showrunner.
Becoming a TV writer is hard, but if you want it bad enough and if writing for the small screen is your passion, then you'll have a hard time giving up on it. Perhaps you'll be the next Tina Fey, Conan O'Brien, or crime procedural writer that no one's ever heard of. But you'll never know unless you're willing to give it all that you've got.