In Austria it is Socialist medicine so I was a little worried about the structure of going into a doctor's office or hospital - which in my time in Austria I got to visit both unfortunately! I had the advantage that my Austrian college had two doctors that they had an agreement with to take American students and speak English with them - even though I think that you most likely will be ok finding a doctor that speaks enough English as many Austrians speak English as well as German.
I had to get weekly allergy shots and so I got to visit the doctors often. It cost me between 20 and 30 euros every time. Doctors in Austria hold crazy inconvenient hours and it can be very hard to make an appointment. My doctors sometimes decided they were not going to work on a Thursday or that they would work from 8am to 11am. Be sure to look at their hours. It is certainly best to call ahead if you can with the language barrier - or get a friend to do so. If you have an appointment you do not have to wait in the sometimes very long lines at the doctors office.
When you go into the doctor's office be sure to bring your passport (sometimes they want it because you will not have a health card issued to everyone in Austria) and your name written down, and if you can look up what you want to get done in German for example the word allergy shot that helps too.You will meet a receptionist just like America and she will fill out paper work and you may have to fill some out on a German form - so the first time it might be helpful to bring a German speaking friend otherwise a hand held dictionary. You will wait until they call your name. For allergy shots I had to bring my serum every time, they did not just hold it at the doctors office.
I went to the emergency room once in Austria and it was a lot less scary than I expected it to be. At a hospital there will be doctors that speak English - in fact I think that the doctor I got was from Great Britain. I had hurt my back falling down marble stairs and had fainted and had needed to go to the doctor to get xrays. I went with an Austrian which helped the process but they had a form that was in English too. You have to remember that health care is socialist so there will be a long line most likely for the Emergency Room (but I don't know how different that is from America.) :) The only thing was that you definitely want to purchase health insurance when you go abroad because it reduced my bill from 2,700 euros... and I had to pay that in full when I was at the hospital! You cannot just hand them some plastic - it needs to have real money on it!