BY LAND:
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.
BY AIR:
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: