Health system
The health system seems to be similar to the UK with state provision available to all and options for private health.
Our experience of the health system is largely limited to doctors and our local doctors clinic at that so it may well be untypical and our experience has been mostly for the children.
Essentially, like the UK, there are local CAPs - primary care centres - which are essentially doctor's surgeries with some space for in-patients (we haven't seen this part so we don't know what it is like).
Appointments (cita or cites in plural) need to be made and you will need to show your health card showing that you are registered. Registration requires a social security number and an up-to-date proof of residence in the city. The doctors surgery is similar to any, anywhere in the world. You shouldn't expect the doctor to speak English - Spanish and Catalan only.
Our children needed an eye check and unlike the UK where this is typically done at an opticians, we were directed towards the doctors as opthamology and optometry are connected with the CAP. To get to see the optometrist we had to be 'referred' by the pediatrician, so needed to see the GP first. With the GP's referal we could then get an appointment with the optometrist, and from her, get an appointment with the ophthalmist. Unfortunately this is when you discover that Spain has similar waiting time problems with the UK with waiting times of around 2-3 months, so even something as simple as a children's eye check can be a long drawn out process. Apparently similar situations exist in Spanish hospitals.
The alternative is private health care. There is an extensive network of private health care clinics in Spain and a large number of suppliers of private medical insurance. As yet we have little experience of either.