To begin, navigate to the Telegram deactivation page, and sign in with your phone number - don't worry, it's quick and painless, I promise! You'll need to enter the phone number associated with your account, so make sure you've got it handy. Then, just follow the on-screen instructions, and you'll be golden!
The process is pretty straightforward, and you'll be asked to confirm that you really want to delete your account - this is your last chance to turn back, so think carefully! You'll need to enter a confirmation code sent to your phone, and then... poof! Your account is gone for good!