No worries, its a nightmare for Americans to figure out as well. It was supposed to be a fix for the fact that the US pays twice as much as other countries for healthcare that isn't better and actually rates lower than places like France. What country are you in?
I'm in France... The system is not perfect here, for instance glasses or dental are not very well covered unless you're very poor. But private additionnal insurance is pretty cheap (my girlfriend pays 15 per month and 50 from her employer) to cover herself, myself and our kid, including dental implants, designer glasses, osteopathy...), since there is already coverage from the state for the really serious stuff (cancer, AIDS...).
We also have a pretty large not not profit private insurance system (mutualistic insurances), that's what I use for my home insurance for instance.
But yes, it's pretty complex too, because we have a mixed private/public system at all levels (insurance, doctors, hospital). But it does give a lot of flexibility: I can pick my doctor, I can change doctor whenever I want or go see a second one for another opinion, I can pick my options for treatment... I never had to wait too much for an appointment, but I live in Paris and we have plenty of doctors. Waiting is more a product of doctors not wanting to work in poor areas or in the countryside rather than of the insurance system.
The system is not perfect, but, yes, compared with the US we get a much better deal...
My opinion on the US reform is that it should be all or nothing. But since the opposition uttered the word "socialist", it ground the reform to a halt. So, you end up with a halfway things where all the public money seems to be forked to private insurance and with no cost control at all. That's a pretty bad mix...
Cost control is a very important part of all European "socialist" system. Since you have a monopolistic insurance at State level, it can enter negotiation with the pharmaceutic industry. It can evaluate if a drug is actually better than the previous generation and decide not to cover it if it doesn't. It can decide that a drug is too expensive for what it does compared to other less expensive drugs and ask that the price be reduced in exchange for covering it fully. The end result is that the price of drugs is usually cheaper in Europe than in the US, even before insurance coverage.
Likewise, the state fixes the maximum damages you can get from malpractice (from a doctor not from the pharma industry). So, you won't get rich from your doctor making an error, but doctors are not ruined from making an honest mistake. So, doctor's insurances are at a reasonable level, which means their prices are reasonable too (typical visit to a general doctor is around 25, specialist will be around 50-70 - before insurance and in Paris where they are usually above the state insurance coverage but private insurance will cover the difference).