Both destinations are served by Dehra Dun (DED). Since there's no flight route between them, the best way to travel is by road.
Paonta Sahib
Fly to Dehra Dun (DED), then travel by road to Paonta Sahib. Taxis, buses, and private cabs are available from the airport.
Dehradun
Fly to Dehra Dun (DED), then travel by road to Dehradun. Local transport options include taxis, auto-rickshaws, and state buses.