You can't actually walk into a service center and order tests. You need a doctor to order them. This is one thing Theranos is trying to change: enable and simplify access to your own medical data.
Are you referring to blood tests, in general, or Theranos tests? I don't know about Theranos, but, in most places (in the US), you can order blood tests without a doctor's orders. See: https://www.directlabs.com/
