The Tribhuvan airport in Kathmandu is Nepal’s only international airport. The main airlines that serve Kathmandu are Indian Airlines, Thai International, Bangladesh Biman, China Southwest Airlines, Druk Air, Qatar Airways, Gulf Air, Jet Air, Etihad, FlyDubai, Air Asia etc. The national carrier - Nepal Airlines Corporation (NAC), operates flights to Europe and Asia as well as regional destinations.
You could travel to Kathmandu via Bangkok, Hong Kong and Singapore. There are daily flights to Kathmandu from Bangkok. If in India, you can fly to Nepal from Delhi, Mumbai, Calcutta, Bangalore and Varanasi. There is the spectacular flight from Lhasa to Kathmandu on Saturdays, Tuesdays and Thrusdays operated by China Southwest Airlines. You can also fly Druk Air from Paro in Bhutan, or take a flight from Dhaka, Bangladesh.
From Europe and Middle East
Qatar Airways, Gulf Air, Oman Air, Etihad and Fly Dubai all operate daily flights to Kathmandu from Doha, Dubai, Abu Dhabi, Muscat and Bahrain. Bangladesh Biman and the above mentioned Middle Eastern airlines all offer flights from various cities in Europe with one stop over in the middle east, India or Bangladesh.
From North America
Any of the Middle Eastern or Asian Airlines will bring you to Kathmandu with a couple of stop over’s in Europe, the Middle East and South Asia.
From Australia and New Zealand, look for routes via Singapore, Hong Kong or Bangkok, usually with hai International.
There are many entry points into Nepal by land open to foreigners, from which most are from India and one from Tibet.
The crossing points from India include Mahendranagar, Dhangadhi and Nepalgunj in the west, Sunali, Birganj and Kakarbhitta in the east. Make sure to book your tickets through a reputed agency to avoid getting duped. Also bear in mind that everyone has to change buses at the border whether they book a through ticket or not, and that despite claims to the contrary, there are no tourist buses on either side of the border. You can board direct buses to the Nepal border from Delhi, Varanasi, Calcutta, Patna and Darjeeling. From the border, you can board Nepali buses to Kathmandu.
You can cross the border into Nepal from Tibet via Kodari.