Yes, the US has stationed troops and nuclear missels in Germany but this is far from "running the shop".
I disagree that the US runs Germany.
Also, the occupation authorities were instrumental in establishing the German intelligence service from the get-go, liberally making use of the existing NS personnel (Wikipedia[1] lists Reinhard Gehlen, Klaus Barbie, Alois Brunner, Wilhelm Krichbaum, Franz Rademacher, Walther Rauff, Konrad Fiebig, Franz Alfred Six as prominent examples).
[1] http://de.wikipedia.org/wiki/Bundesnachrichtendienst#Geschic...
And yes, the US army bases in Germany are left overs from the allied occupation after WW II
As with any other country with a large standing army (Germany sits somewhere between South Korea and France in terms of capabilities), it would probably begin with large scale air strikes with stealth bombers against military targets. Within the first 4 hours, most militarized airfields and radar installations would be destroyed. The ground forces would invade from probably Italy and Poland, both highly US dependent states, assuming that France and the UK would stay neutral in such an attack. You'd probably see some guerrilla warfare because the Germans are strong-willed, but the vast majority of the population is westernized enough to not put up a real fight. But none of this would happen until the US has at least 2 carriers in the Baltic Sea, so Germany would definitely have advance warning, and hopefully the foresight to negotiate.
Germany has no nuclear deterrent, as it simply hosts US missiles by way of NATO [2].
EDIT: This spells it out pretty clearly, the US has more helicopters than Germany has tanks ships and planes combined: http://www.globalfirepower.com/countries-comparison-detail.a...
1. https://www.cia.gov/library/publications/the-world-factbook/ 2. http://www.rusi.org/publications/occasionalpapers/ref:O4B991...