There is only one international airport, Tribhuvan International Airport and it has direct flights to and from the following countries: 1) Singapore (Silk Air) 2) Korea (Korean Air) 3) UAE (Nepal Airlines, Etihad Airways) 5) India ( Nepal Airlines, Jet Airways, Jet Lite, Indian Airlines, Druk Air) 6) China (Air China, China Southern Airlines) 7) Thailand (Nepal Airlines, Thai Airlines) 8) Bangladesh (Biman Airlines, GMG Airlines) 9) Pakistan ( Pakistan International Airlines) 10) Bhutan (Druk Air) 11) Bahrain (Gulf Air) 12) Malaysia (Nepal Airlines) 13) Qatar (Qatar Airways). Basically travelers from all over the world, may it be the USA, Europe coming to Nepal via connecting flights from the above locations.
You can also get to Nepal by road from southern India, and north China. You could travel by train or bus to the Indian-Nepal border and then by road to reach various cities in Nepal. You can travel from Delhi to Banbasa, a village on the Indian border, by bus for about eight hours. Then take the bus from Mahendranagar to Kathmandu which takes another 15 hours. Alternatively, you can travel by train to Gorakhpur from Delhi (16 hours) and take a bus from Gorakpur to Sunauli (3 hours). Then you can travel from Bhairahawa, a town on the Nepal border to Kathmandu, Pokhara.
You can also travel from Kolkata to Raxaul by train (15 hours). You can also travel from Patna to Raxaul (7 hours) by bus. Then take the bus from Birgunj, a Nepali border town near Raxaul, to Kathmandu (10 hours), Pokhara (9 hours). You can travel from Darjeeling to Kathmandu via Kakarbhitta, a town on the Nepal border. You need to travel from Darjeeling to Siliguri, then from Siliguri to Panitanki (1 hour). Then cross the border to Kakarbhitta and drive to Kathmandu by bus (14 hours).