There are different ways to enter in Nepal that include by Land and by air. As Nepal is a landlocked country, it doesn't have sea routes.
If you want to enter in Nepal by land, you can get into from India and Tibet. From Tibet, you have to cross the border at Kodari and take a bus to Kathmandu. It is about 7-8 hours drive to reach Kathmandu, the capital city of Nepal. From India, take a train from Gorakhpur and from Sunauli/Belahiya border, then take a bus to your destination. To enter in Nepal, some other borders of India are Birjung/Rakshaul, Kakarvitta and others.
The only international airport in Nepal is the Tribhuwan International Airport in Kathmandu. There are several airlines that fly to Nepal. See the lists of those airlines:
Beside these there are Biman Bangladesh, Jet Airways, connecting Kathmandu with many countries.