Germany is a member state of the so-called Schengen area, which includes most EU countries and Switzerland (but excludes e.g., the UK). Since there are no regular border controls between Schengen countries, immigration is done in the first Schengen country you enter during your trip. For example, if you fly in via Amsterdam or Paris, immigration will be made there.
For citizens of EU countries, the national ID card is sufficient for entering Germany, participants from most non-European countries will need a passport. Please inform us if you need a visa; US, Canadian, Japanese or Australian citizens won't need a visa.
The closest airport is Frankfurt international airport (airport code FRA). FRA has two terminals. Terminal 1 is used by Lufthansa, United and their partner airlines (Star Alliance), Terminal 2 by KLM, Air France, Delta and their partner airlines (SkyTeam). Both terminals are connected by an automated train system (follow the signs directing to SkyLine) and free shuttle buses stopping in front of the terminals.
There is a direct shuttle bus named AIRliner connecting Darmstadt railway station with terminals 1 (Bus stop no 14, arrival level) and 2 (in front of the terminal). Travel time is about 30 minutes. The ticket price is 8.35 Euro. You need to buy the ticket in cash when entering the bus, thus you should get some cash when arriving at FRA (and best not just 50 Euro notes). When travelling back, you may purchase an AIRliner ticket at any ticket selling machine in Darmstadt. The bus will end in front of the main railway station. The easiest way to plan your trip is to print out the PDF flyer provided by the local traffic company, including the whole time schedule.
A taxi to Darmstadt will be about 50-55 Euros.
There are some companies in DA offering shuttles to or from the airport. When going to the airport it's very convenient, normally you may order them online and they'll pick you up at the requested time and place. Transfer from the aiport is a bit more complicated. Since they aren't allowed to wait at the taxi line of the airport, they normally require that you phone them when you actually arrived at the airport, hoping that they will make the trip to the airport while you are waiting for your luggage. Anyway, here are two shuttle companies that have at least English info:
The Frankfurt-Hahn airport (code HHN) is also reasonably close by, with connections to many places in Europe via Ryanair and other low-cost carriers. It's about 2.5hrs from Darmstadt by bus (change in Frankfurt), or 1.5hr by rental car, but the cheaper airfares may be attractive. Another airport used by low-cost airlines is Köln-Bonn (Cologne, CGN) that has a fast train connection to Frankfurt (1hr).
Darmstadt is connected to Frankfurt, Heidelberg, Stuttgart, Karlsruhe by InterCity trains. By regional trains, you may reach Darmstadt from Frankfurt, Mainz/Wiesbaden, Mannheim, Heidelberg, Aschaffenburg. You may plan your trip using the web site of Deutsche Bahn. If you arrive at Darmstadt, proceed to the main entrance (that's a left turn when leaving the platform), where you can reach a bus, streetcar or taxi.
You may take the bus or streetcar to reach the hotel. Please use "Darmstadt Schloss" as destination. You may go there with the streetcar lines 2, 3—since Hauptbahnhof is their final stop, you are on the safe side when using these lines since you can't use the wrong direction of travel, or bus lines H (direcion Kesselhutweg) and K (direction TU Lichwiese). There is also streetcar line no 5 starting at the railway station, but you would have to use the exit Willy-Brandt-Platz (just a short walk through the park named Herrngarten) since this line doesn't stop at Schloss. You may wish to print a map of transport in Darmstadt.
Darmstadt is member of the Rhein-Main traffic organisation (RMV). If your starting point is within the RMV area, you only need one ticket from starting to end point. This is also the case if you bought an AIRliner ticket at Frankfurt airport, i.e. the AIRliner ticket is also good for the bus or streetcar trip from the railway station to the hotel.
If you need to buy a ticket: these may be purchased for 2 Euro at ticket machines, in buses they are also available from the bus driver. No tickets are sold within street cars. Please keep in mind that using busses or streetcars without a valid ticket will yield in a 40 Euro fine if you are caught.
When leaving the bus or streetcar at the south side of "Schloss" (castle), adjecent to the "Marktplatz" (market place), the shortest way to the hotel is just going through the castle, since the hotel is located directly on the castle's north side.
For those who want to go around by bus or streetcar within Darmstadt: Darmstadt is separated into three fare zone. Zone 4001 is central Darmstadt, including the city center, Mathildenhöhe, Rosenhöhe, railway station, so normally buying a ticket for 4001 is sufficient. A single ticket is 2~EUR, a day ticket 3.90~EUR. Nothern Darmstadt with the suburbs Arheilgen, Kranichstein and Wixhausen is zone 4035, southern Darmstadt (DA-Eberstadt) is zone 4045. Single fare from 4001 to 4035 or 4045 is 2.45~EUR. All Darmstadt zones build the zone 4000. A single trip for zone 4000 is 3~EUR, a day ticket 5.85~EUR, a week ticket 25.30~EUR, allowing you to go from anywhere in DA to anywhere in DA.
Map created from Openstreetmap.