Limburg an der Lahn Transportation

You can easily reach Limburg by train. There are connections from Frankfurt, Köln (Cologne), Koblenz and Gießen. The railway from Koblenz to Gießen via Limburg is along the river Lahn, really nice!

From Frankfurt, you can take the ICE (intercity express). It's about 20 minutes then (from Frankfurt airport). Unfortunately they run only every 2 hours. And please note that the ICE station is outside of Limburg. Do not confuse it with the station in the centre of Limburg! There are busses from the ICE station to the center, though.
You can also take a "usual" train from Frankfurt. From Frankfurt main station, it's about 1 hour drive, and you will arrive in Limburg at the station in the centre. Direct trains usually run once a hour (sometimes more often). It's also possible to take the S-Bahn number 2 to Niedernhausen and frome there take a train to Limburg.

From Köln/Cologne, the fastest way by train is to take the ICE. It takes about 40 minutes and you'll arrive at the ICE station in Limburg. Trains run about each hour. Another possibility is to go via Koblenz, but although you'll see nice landscapes, I'd rather prefer the ICE - it's much faster!