You can fly between Delhi and Kathmandu, there are many flights available in this sector. There are a number of overland entry points for travel by road and you could come by train to Ghorakpur, travelling the rest of the way by road.
Please note that Delhi-Kathmandu-Delhi flight is very busy and without proper reservations in advance it might be difficult to get seats.
Alternatively, you can travel overland to Nepal from India by bus. There are three main entry points: Sunauli-Bhairahawa, Birgung-Raxual and Kakarvitta. The Sunauli border crossing is the best option to make your entry into Nepal from Varanasi; the Birgunj crossing is the easiest from Calcutta and Kakarvitta is the best crossing point from Darjeeling and Sikkim. These overland trips from India can be quite long and stressful and are not recommended for those people who want to have stress-free travelling.