For the "insert patient" operation, I'd suggest something like a POST to /patients (if the server generates the patient ID) or a PUT to /patients/{patient-id} (if the client generates the patient ID). Either way, the body of the message would contain all of the input data needed to create a new patient entity. Two simple options for serializing the data would be as a URL-encoded form or as JSON.
Lookup by by ID could be a simple as a GET on /patients/{patient-id}. Lookup by address could also be a GET, possibly using a URL-encoded query parameter. For example, you could fetch the patient at address "123 Main Street, apt 4, Anytown, USA, 98765" with a GET on /patients?addr=%20Main%20Street%2C%20apt%204%2C%20Anytown%2C%20USA%2C%2098765