My personal experience with Czech medicine is so far quite positive and unproblematic. I have a protracted problem with my ear, so in my case there was nothing urgent. At first, I wanted to visit a private clinic (I am used to do that in Russia — our public hospitals are something of a nightmare), but I was afraid that my insurance company will not give me a refund for that, so finally I ended up in public hospital, specifically Nemocnice Motol. First thing that a foreigner should do is to go to foreign department (schedule is on their website) and fill some documents for your insurance company. After completing those I waited in a queue for about 15 minutes (doctors take patients with acute issues first). My ENT doctor was very supportive and kind, she spoke quite fluent English and did all examinations possible, in the end she also gave me prescriptions for medicines. In general, the place was very up-to-date, clean and amiable, so I recommend not to be afraid of visiting public hospitals in Prague.