How can one delete their instagram account?

After you delete your account, you can't sign up again with the same username or add that username to another account, and we can't reactivate deleted accounts. Go to the Delete Your Account page. If you're not logged into Instagram on the web, you'll be asked to log in first. You can't delete your account from within the Instagram app. Select an option from the drop-down menu next to Why are you deleting your account? and re-enter your password.

The option to permanently delete your account will only appear after you've selected a reason from the menu. Click or tap Permanently delete my account. If you'd like to delete a different account, click the username in the top-right of the Delete Your Account page, tap/click on next to username and select Log Out. Log back in as the account you want to delete and follow the directions above.