Airport
The closest airport is Nuremberg Airport (NUE).
Public transport from the airport
It takes about 45 minutes from the airport to Erlangen Central Station by public transport. For real-time information, check the website of the local transit authority.
Train connection: Take the U2 subway line and get off at Nuremberg Central Station (Nürnberg Hauptbahnhof). From there, there are various regional trains which stop at Erlangen station. The fare is 5€.
Bus connection: Take bus line 30 in the direction of Erlangen, which goes directly to Erlangen Central Station. The fare is 3.70€.
Taxi: A taxi ride from the airport takes about 25 minutes and costs around 38€. (Tipping in Germany: Just round up to the full euro or pay 1-2€ of tip for such a ride - that's the usual way.)
From the train station it is a 5 minute walk to the Orangerie. See the map here: