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