The closest international airport is Frankfurt airport (FRA).
From there, you can reach Darmstadt conveniently by bus called AirLiner (Download flyer as pdf). The bus stops at Darmstadt main station (Hauptbahnhof), and also at Darmstadt convention center (darmstadtium) (the last bus stop, which is located close to the university). The AirLiner departs in Frankfurt airport from Terminals 1 & 2. If you arrive at Terminal 1 follow the signs "Bus station" and wait outside at platform #14. If you arrive at Terminal 2 follow the signs "Arrivals Area D+E" and wait outside at the next bus stop. The AirLiner is a big yellow bus with two floors. You can buy tickets directly from the driver which cost around 9€.
Also see the map: The main station is right next to the InterCity Hotel, the Darmstadt convention center (the final stop) is right across the street from the Welcome Hotel.
To get to your hotel, take the AirLiner:
To check train schedules and fares, see German Rail.
Please note that tickets for regional trains are not valid in ICE, IC and EC trains. For the latter, you need special (and more expensive) tickets. The ticket vending machines show the available connections, and it's easiest if you buy a ticket for the exact connection you are going to use. See the local information page for more information on how to reach your hotel from Darmstadt main station.
See also the local information page.
See the local information page for a map.