The nearest airport is in Simferopol. There are direct flights between Frankfurt and Simferopol. Transit via Kiev, Moscow, Odessa, St.Petersburg, Istanbul and Tel-Aviv are also recommended. There are many international flights to Kiev and several daily flights and overnight trains from Kiev to Simferopol.
It is also possible to reach Alushta by railways. The railway station in Simferopol is about 50 km from Alushta.

See the following links for airplane and railway schedules in Ukraine.

Local transportation from Simferopol airport and railway station will be provided by the Organizing Committee on the arrival and departure dates. Otherwise the school place can be reached by bus, trolleybus or taxi.

People from many countries do not need Ukrainian visa for a short stay, such as: USA, Canada, Japan, EU nations, Switzerland, Liechtenstein, Andorra, Vatican, Iceland, Monaco, Norway, San Marino, Mongolia, Lithuania and the countries of the Commonwealth of Independent States (except Turkmenistan).

Please check carefully regulations applicable to your case at this link and, in case you will need a visa, please ask the Organizing Committee for corresponding invitation.