There are a number of airlines that fly into Kathmandu’s Tribhuvan International Airport. The links below are for the airline’s main site, however tickets may be found cheaper elsewhere.
For onward travel to Bhutan, Somewhere Different can arrange your visa and tour.
Entry into Nepal by land from India can be made at the following border crossings:
Sunauli to Belahiya
Raxaul Bazar to Birganj
Gauriphanta to Dangandhi
Panitanki to Kakarbhitta
Banbasa to Mahendranagar
Jamunaha to Nepalganj