Although you don't need to be an athlete to trek in the Nepal Himalaya, some degree of fitness level is required. The better shape you are in, the more you will enjoy the trip. Trekking is about taking your time, setting your own pace and enjoying the experience to its fullest. Its common that most first-time trekkers are concerned that they won't keep up, but soon discover that a steady pace will have them in camp well before they would have expected.
Trekking in Nepal Himalaya is not like a race or walking contest but a walking holidays for people of all ages. Trekking hours can be as short as 2 hours and as long as 7-8 hours in an uneven terrain. The trail can be steel uphill or downhill and at times crosses rivers and springs by suspension or wooden bridges. Enthusiasm for walking and mental preparedness play the vital role.
You may be at the best shape but if you have no interest in walking, trekking is not for you. With a little training exercise and enthusiasm, you can participate on any trekking trips in Nepal Himalaya. There is no one size fits all kind of training program. Everyone is different. There is no better training than trekking itself. Get a day pack on and get out there as often as you can. But if, like most people are, you are limited with free time, you can do short power exercises like jogging, swimming, cycling, aerobics etc which you need to start 2-3 months prior to the trip date. The exercises strengthen your muscles and builds stamina and confidence for the trekking. If you can manage a couple of valley floor to ridge line ascents per bushwalk, you will cope with a moderate graded trek. Speed is not the essence; stamina, confidence and continuity are.
However, if you are planning to join a commercial trekking or mountaineering expedition you will need to develop a high level of fitness so that you can comfortably and safely endure several weeks on the trail.