You can go for overland travel to enter Nepal from both India and Tibet.
If you are in Tibet, you can enter Nepal by crossing the border at Kodari. Thereafter, take a bus to Kathmandu. This will take you 7 to 12 hours depending on the road conditions.
The easiest and hassle free overland route to Nepal from India is via Gorakhpur using train and the Sunauli/Belahiya border post. The only direct buses from this route to Kathmandu run at night and take approximately 9 hours. Raxaul/Birgung border post can also be used to visit Nepal. But this may not leave you with a pleasant travelling experience. If you are in Darjeeling you can come to Nepal via Karkabhitta. There are also several border crossings in west Nepal.
Kathmandu is the only international airport in Nepal till today but there are few other airports under construction outside Kathmandu city. There are a number of International Airlines with direct flights to Kathmandu. Thai Airways International operates daily flight between Bangkok and Kathmandu. Qatar Airways flies daily between Doha and Kathmandu with connecting flights to/from Europe and America. Gulf Air has daily flight between UAE and Kathmandu with connecting flights to/from Europe and America. Air China flies between Lhasa, with connecting flights to/from mainland China. Austrian Airlines flies between Vienna and Kathmandu once a week Indian Airlines have frequent flights between Delhi, Calcutta and Kathmandu.