Kathmandu, the capital city of Nepal, can be easily reached by air from many Asian and Middle Eastern transport hubs, as well as rather laboriously overland from India and China (Tibet). Here's what you need to know about getting to Kathmandu.
By Air
Kathmandu's Tribhuvan International Airport is the main international airport in Nepal, so the vast majority of travelers arriving in the country by air do so via Kathmandu. Many major international airlines, as well as a number of smaller Asian and regional airlines, fly to Kathmandu.
If coming from somewhere very far away, like North America, Europe, or Australia, you will have to transit through an Asian or Middle Eastern air hub, such as Istanbul, Dubai, Qatar, Delhi, Singapore, Kuala Lumpur, Hong Kong, or Bangkok. It's also possible to fly into Nepal from smaller regional centers, like Dhaka, Lhasa, Varanasi, or Paro.
Getting to Kathmandu by air is by far the easiest and most comfortable way.
Overland From India
While Nepal and India share many border crossings along Nepal's western, southern, and eastern border with India, many of these are only open to Indians and Nepalis, not other nationalities. The main border crossing is at Birganj-Raxaul, which connects Birganj on the central Nepali Terai (south-west of Kathmandu) with Raxaul in India's Bihar state. This is open to non-Nepalis and non-Indians.
If you are traveling around the North Indian states that border Nepal (to places such as Varanasi, Sarnath or Patna), it's possible to get local buses to various border points, and then continue to Kathmandu on a Nepali bus. Be sure to double-check that the border you're going to will allow non-Nepalis and non-Indians to cross.
A more common way of making the overland journey is from Delhi. A range of Indian and Nepali bus companies operate a bus service between the two capitals. Tickets are cheap, with varying levels of comfort depending on the class of service. Most cross at the Birganj-Raxaul border after traveling through Uttar Pradesh and Bihar from Delhi, but some head east from Delhi, cutting through Uttarakhand and entering far western Nepal, crossing the Mahakali River.
The Delhi to Kathmandu bus trip is very long, at more than 30 hours. The highways through India are of a decent quality, which deteriorates noticeably once you cross the border into Nepal. During the summer and monsoon, even air-conditioned buses won't necessarily be able to keep the heat of the Indian plains at bay.
The journey is not comfortable, but it's quite an experience—best suited to adventurous travelers who are on a limited budget or aren't in a hurry. You're unlikely to encounter many other foreign tourists on the trip, but many Indians and Nepalis traveling between the countries for business or pleasure.
Overland From China (Tibet)
Kathmandu can also be approached overland from Tibet, as Nepal shares its entire northern border with China. The experience is very different from traveling overland from India. For one, almost all foreign travelers must tour Tibet with a guide, on an organized tour (although this doesn't necessarily mean with a group of strangers). So, for at least the Tibet portion of the overland trip, you'll be traveling in a private vehicle.
The roads in southern Tibet are generally very good, so it's possible to travel quickly from cities like Shigatse and Lhasa. The main overland Nepal-Tibet border crossing these days is at Kyirong-Rasuwagadhi, around 90 miles (150 kilometers) north of Kathmandu. The border is sometimes closed by the Chinese authorities. You'll have to change vehicles at the border, but if you are traveling on a guided tour, you'll be helped through this process.
The road from the border to Kathmandu is in extremely poor condition in some places, and only moderately poor condition in others. The journey from the border can take as few as seven or eight hours if there are no accidents, landslides, or extensive mud on the road (during the monsoon), or much longer if there are. A much quicker, more comfortable way of getting to Kathmandu from Tibet is to fly from Lhasa!