When you cross from Germany in to Austria, do you purchase the vignette there at the border crossing?
Yes, you can buy them at border posts, and you can buy them at many fuel stations before the border, especially on Autobahns.
But, you only need a Vignette if you are driving on Autobahns. And because Austria and all surrounding countries are part of the Schengen area and (except Switzerland) part of the EU, there are often no border posts. If you cross on a minor road (not an Autobahn) you may need to go searching. In that case ask at the first fuel station you see over the border.
At the border points near Salzburg and Kufstein there are stations where you can stop and purchase the vignette. Often the vignette is sold also at petrol stations in Germany well before getting to the border.
Be extremely careful, as Austrians will not force you to buy a vignette but they are likely to put a control point a few miles past the border, and fines are stinging. If you do not have a vignette do not even try to go on on the highway.
Not usually. Look for it within about 20 km or so from the border at German petrol stations or Autobahn service areas.
Huge signs outside with a photo of the vignette blown up about 500 times and the words Vignette Hier or similar. Pop in, tell them that you want a Vignette for your car/bus/trailer/motorcycle, and for how long (minimum 10 days, about €8) and they will punch the start day on it and hand it to you. Writing on the back in English and other languages, and illustrations of where to put it on the windscreen. You have to have it stuck on, and in the right place or the robo-cameras will think you didn't buy one and send you a love note.
Depending on where and how far you are driving, planing using the secondary roads you may not need to travel on the Austrian Autobahns. Top speed is 130 kph. Many places the secondary road parallels the Autobahn. I was recently on E45 and the speed limit was limited to 100 kph. The 10 day Vignette was only euro 8,00 for a car though. We bought ours in Germany at the last rest stop before the boarder and you can't miss the signs, and there are directions on the sticker as to where to put it on the windshield as mentioned.
As mentioned before, there are no official "border" crossings unless you're going into Switzerland. We'd never traveled between countries before & the borders were less marked than our state lines! We drove into Austria on May 14th from the eastern end of Lake Konstanz (Bodensee). We purchased our vignette the day prior from a stop in Switzerland. They only sold 15 day ones for 10.20 Swiss Francs.
Note that if you are going to drive the E60/A14/S16/A12 across Austria & go through the Arlburg Tunnel, you will have to pay an extra €9.50. We were traveling east, so the toll plaza was at the east end of the tunnel as we exited it. Stations are manned, so you shouldn't have to worry about exact change; tho we didn't know it at the time! The tunnel is about 14 km long. There are horror stories about it, but we found it to be terrific. May 14th was a Saturday.
Hope that all helps!