A generally good level of physical fitness is a must for you to be able to set out on a trek. Because you have to walk for longer hours and ascend to altitudes you are not generally used to with, you require high endurance level. You definitely would not want to be in a situation where you cannot fully enjoy the trek because of your fitness level.
For climbing, the requirements get tougher. Apart from being physically fit, you have to have some prior experience in climbing. For trekking peaks, you will get the basic climbing training once you arrive in Kathmandu. However, if you are attempting higher peaks, you would not want to be a first timer.
For more information regarding how to build your fitness level for trek, you can visit the website www.trekkingfitness.com. Its founder Alex Shirley has put up some very nice and convenient exercises that help you get your fitness level up for the trek.