One of the first things it would be advisable to do is to register with your local health centre. Even if you intend to use private health insurance there are circumstances where you could be required to visit the public health doctor e.g. where you are off work due to illness you are required to obtain a ‘baja’ in order to receive (a proportion) of your salary while sick.
How to apply for a Medical Card
In order to obtain your medical card you just need to call into your local health centre with your Social Security Number your passport and certificate of empadronamiento (some may ask for a certificate of residency but strictly speaking this is not necessary).
You will also be asked for your NIE number and details such as your address etc.