My girlfriend is a U.S. citizen and I'm taking her on a trip through Germany (I'm German). She will enter the EU at Frankfurt airport as a tourist. During our trip, we want to go to Lake Constance, where I'd like to go around the lake which means we'll be briefly in Austria and Switzerland. Austria is of course no problem, as it is part of the EU. What about Switzerland? Can she enter Switzerland without further ado, or is there something we need to do beforehand?
Yes, Switzerland is part of the Schengen area, so you will have no trouble traveling there, provided you remain within your 90 days of 180. You will still see border checkpoints for commercial traffic, as Switzerland is not part of the EEA, but you should not be affected.
You need to pay a highway tax (about 30 Swiss Francs) if you plan to travel by car on national highways. Provincial (Canton) highways are not effected by this tax. The sticker is valid for one year (for example year 2015). A national highway can be easily recognized. The signs at the entrance and at the exists are green, otherwise they are blue. The sticker must be attached to the front windshield. Driving on national highways without this sticker is very expensive.
The rules for Switzerland are almost the same as for Austria. The country is part of the Schengen area, which means it honors Schengen visas (or visa-free visit rules for US citizens) but also that the days spent in the country count towards the 90-day duration of stay limit for your girlfriend.
Even if you often see border guards standing around, most of the time, there is no passport check at the border. In some cases, mostly on smaller roads, the border is even completely open (there is a sign but no building and no guards).
The main difference between Switzerland and EU member states are the rules regarding the import of goods. You are not allowed to take as much alcohol, tobacco, meat, etc. with you as you would going between Austria to Germany. Those rules obviously apply in any case, even if the border is not guarded.
If crossing by car, I suspect border guards are also on the look-out for people who do not have the motorway vignette (more info on ch.ch). It's basically a sticker that costs CHF 40 and allows you to drive on all Swiss motorways for a year. That's completely unrelated to the rules about entering the country for foreigners but in practice, taking the right lane/stopping to buy the vignette is basically the main thing you need to take care of when crossing this border.
Austria has a similar system but in this case, you need to stop at a petrol station to get the sticker as the motorway just crosses over with nothing else than a sign: no guards, no check, no office/shop, in fact no building and no need to slow down specifically for the border.
It's not what you plan to do this time but if you would want to stay together longer than 90 days, it might be interesting to know that you can do it under EU free movement rules, also in Switzerland, but you would then need some paperwork (a residence card for her, a proof that you have a job or financial means for you).
No problem at all! The Schengen visa will suffice. I did the same thing with a Japanese girlfriend once ;-)