How to reach Erfurt city?
You can fly to the nearest major hub, that is the Frankfurt am Main Airport (FRA), and then take the high-speed train (ICE = Inter City Express) directly from the station of this airport for an approximately 2.5-hours train ride to Erfurt main station.
Alternatively, you can approach Erfurt city via its own small international Erfurt airport (ERFAPXH) with direct connections to/from some major international airports including Munich, Hamburg, Berlin, and Duesseldorf/Köln-Bonn airport.
How to reach Erfurt main station from Erfurt airport?
From Erfurt airport you can either (1) take a taxi; or (2) use public transportation. In case you prefer public transportation you have two options: (a) take the bus line 91 or 92 departing from Flughafen-Büropark (all days), and change at the bus stop “Hauptfriedhof” to the tram line no. 4 direction “Hauptbahnhof”, or (b) Monday - Friday: take the shuttle bus line 99 (direction “Hauptbahnhof”, bus stop of line 99 is situated in front of terminal B; bus line 99 is not operating on saturday/sunday/public holidays).