The nearest commercial airports are in Igarka to the south and Norilsk to the west. Note that Dudinka (as well as Norilsk) are closed cities and have major travel restrictions for foreigners and Russian citizens alike; be sure to apply for a special permit far in advance and to have a darn good reason for the application.
A very limited road network connects Dudinka with Norilsk, including the airport, and Talnakh further to the east. Buses ply the route several times per day. There is a railroad connecting all three cities too but nowadays it's limited to freight traffic.
Dudinka is a large port with cargo ships arriving from all over Russia and beyond, some ships accept passangers. Just don't except it to be possible to get the permissions without extensive skills in navigating through russian bureaucracy. A more viable option is to hop on a ferry from Krasnoyarsk, the shipping company PassazhirRechTrans  usually have three to six departures every month during the summer season. The journey along the mighty Yensei river takes three nights and scenery along the route are spectacular.