In order to fly directly to Nepal from your home country, Tribhuvan International Airport (TIA) in Kathmandu is the only international airport in Nepal. TIA has direct airlink with Osaka, Shanghai, London, Frankfurt, Hongkong, Singapore, Bangkok, Delhi, Dubai, Bombay and Calcutta. Lufthansa, Royal Nepal Airlines (RNAC), Air India, Singapore Airlines, Thai are the airlines that carry most of the foreign travelers into Kathmandu; and if you buy tickets from any other airlines, you will probably connect with one of these airlines for the final leg of your flight.
Alternatively, if you have time and enthusiasm, traveling overland to Nepal via India is an option.