In NZ for basic healthcare, you call to make an appointment with your GP, go in later that day, they give you a prescription and you pay $5 for the medication and about $40 for the appointment.
For specialists in the public sector, there is a long waiting period, like a few months sometimes. You can pay for a private specialist, but it is of course expensive. Completely depends on the type of specialist etc.
Dental is not covered by public health care because we still live in 1864 apparently where barbers are meant to be pulling our teeth, but we are getting very close to having dental as part of public healthcare.
A huge amount of medication is subsidised here, basically anything life-saving like insulin, asthma medication, etc. I have an infinite supply of paracetamol because I just get it prescribed when I go to the doctors and pay nothing for it.
It really blows my mind that the US has an objectively vampiric and unfair healthcare system.