Though different regions of Germany and Austria have subtle variations in dialect, there are a few general, overall differences between High German (Hochdeutsch) and Austrian German, both in vocabulary and pronunciation.
One obvious difference is the Austrian use of "Gruess Gott" (pronounced "groose got") instead of "Guten Tag" or "Hallo." In Bavaria, Germany, "Gruess Gott" is also used often . If someone greets you with "Gruess Gott," rather than "Guten Tag," they are most likely from Austria or southern Germany. The Bavarian dialect is similar to some Austrian dialects, but that is the only exception that would make distinguishing an Austrian accent from a German one more difficult.
When greeting someone with a handshake, it's common to say "Gruess dich," which is pronounced "Griass dee" (rolling the "r") in Austria. "Servus" is also popular.
The Austrian accent makes recognizing and understanding some German words more difficult; knowing some basic characteristics of Austrian pronunciation will help you to understand what a person is saying.
So if JFK had spoken German with an Austrian accent when he visited Berlin, he would have said, "I bin a Berliner."
Many Austrians like to use the phrase "Pfir di" ("pfeer tee") when ending a phone conversation, or just saying goodbye to someone in person. "Wiederschauen" (vee-der-shau-win) is often used in place of "(auf) Wiedersehen." "Ba-ba" is fairly common, much in the way "bye-bye" is used in English. "Ciao" and "Tschuess" ("chewse") are, like in High German, used in Austrian German as well.
For a native speaker of English who has learned High German, Austrian German may sound like a completely different language. The sound of Austrian German is not as harsh as High German, and has a melodic, lilting quality to it. The words tend to flow together much more than in High German, and enunciation and grammar are not all that important. If you can get used to the Austrian dialect -- and even learn how to speak it yourself -- you can claim to have a whole new language under your belt.