Here's how to say goodbye to sepia filters and walk away from Instagram, without any trace.
To delete your Instagram account, visit
Instagram.com and sign in to your account. Next, select your account name in the upper right corner, and then select Edit Profile.
On the resulting page, scroll down, and look for the link labelled "I'd like to delete my account." Instagram will ask you why you want to delete your account--though not before referring you to a page to soothe your concerns about its privacy policy changes.
Select your reason you are leaving Instagram, then enter your password where prompted, then press but button labelled "Permanently deactivate my account."
NB:
Keep in mind that Instagram doesn't have an account deactivation feature like Facebook where you can revive your account later (which admittedly seems a little wonky considering Facebook owns Instagram), or a reactivation grace period like Twitter has.
Once you press that red button, your account--and everything you've published to it--will be permanently removed, and you won't be able to recover it or reuse your old account name. So before you press that button, make sure that you never want to see a sepia-filtered square photo of a really good latte again.