I can't say I know much about your particular visa policy, but the general broad strokes of NHS care are these:
First port of call is usually a self-help approach in regards to minor ailments and common conditions. You can get walk-in advice and guidance from most pharmacies and they stock a wide variety of basic non-prescription medicines.
Also, you should be registered with a general practitioner (a doctor based in the community in the local GP surgery"
. These doctors manage the day to day of chronic health problems and are usually the first port of call for healthcare. Contrary to other countries, our GPs have a very good broad knowledge and will manage pretty much anything and will refer on to in-hospital specialties if treatment is refractory or is particularly specialist/technical/invasive. Also they can refer on if a patient needs to see a specialist for an operation/surgery. There may be some element of picking and choosing with regards to broad geography, but not usually.
GPs arrange blood tests, xrays, MRIs etc and can signpost to various other more specialist community clinics like counselling, GUM/STI clinics/midwifery etc. They also deal with contraception and pregnancy.
Prescriptions are a little complicated. Broadly speaking there is a fixed prescription charge but there are many exceptions that you should have a read about.
Then in emergencies, you have urgent care centres, minor injury units and A&E (emergency department). You can use the NHS direct website or call 111 for advice on which service is most appropriate. Obviously if there is collapse, stroke, life threatening bleeding etc you would call 999 for an ambulance.
All of the above is free through the NHS but there is an option to go private with many things if you're willing to pay for it.
Dental services are again NHS led, but not free. You typically have to pay various fixed rates for check-ups and different levels of treatment, but it is largely subsidized.
The NHS doesn't cover things abroad as such but there is a EHIC scheme for certain things/locations, but I'm not sure if you would be entitled to that.
Thats about it really.