The direct express train will get you to
Moscow railway station. Express trains circulate every 20-30 minutes.
The tickets can be bought in the airport building, in the book-office near the exit to the train platform.
Then one should get to the Savelovskiy railway station.
The best way is to use metro to the Savyolovskaya metro station.
From Savelovskiy railway station one can get Dubna by express train or bus:
From Savelovskiy railway station (near Savyolovskaya metro station)
one can get the train to Dubna.
See the time table.