To delete your Telegram account, you'll need to head to the Telegram website and sign in with your phone number. From there, you can request a deletion link that will be sent to your phone. Easy peasy, right?
Once you've got the link, just click it and confirm that you want to delete your account. You'll be asked to enter a confirmation code, and then... poof! Your account is gone. It's like it never existed in the first place!