Nepal is a long way from home for most trekkers and getting there will relieve you of a great deal of your hard earned money. You probably dont need me to tell you to prepare yourself well, travelling in asia is fraught with all kinds of problems so ensure that you have done your best to prepare for the unexpected.
The Himalaya form the backbone of Nepal and there are many different areas to visit. Get yourself a couple of guidebooks and surf the web to determine which area suits your requirements. If you want to get away from it all and not be surrounded by hundreds of fellow trekkers don't go to the Annapurnas in peak season!
October and November are the peak trekking months. The weather is usually fine and the skies clear, the nights can get cold and will be below freezing at higher altitudes. In the winter period from December to February many of the high passes are closed and some treks such as the Annapurna Circuit are impossible. The Spring trekking season has good weather but the skies can get quite hazy. Many parts of the Himalaya are covered with spring flowers at this time so if you have a botanical bent then perhaps Spring is the best time for your visit.
There are two choices here, either you go on a group trek organised by a reputable trekking company or to quote Fleetwood Mac, you can go your own way. Some organised treks take care of everything, including your flights, others start in Nepal, usually Kathmandu. Organised trips are great if you have a limited amount of time, everything is planned out in advance and many of the things that could go wrong are dealt with for you. I have been on two group treks, both with Exodus Travels and their experienced trek leaders and local Nepalese staff ensured that the treks went as smoothly as possible. Whilst in the Khumbu, one of our group had to be helicoptered back to Kathmandu, this would have been very difficult to organise personally. Group treks do have their disadvantages though, they are relatively expensive and the pre-planned itinerary can cause problems if you fall ill along the trail. Again because of the tight timescale often there is not enough time to sit and take everything in. On my Everest trek we had about an hour in Tengboche, I could have happily stayed there all day soaking in the atmosphere and unwinding.
Make sure that you visit you doctor early enough for him/her to organise an immunisation plan.
You will need a visa for Nepal. These are issued for different periods, e.g., 15 days or 30 days. If you plan to go with a trekking company they may provide a service to help you with this. Otherwise you will need to contact the Nepalese Embassy or Consulate in your country to find the current rules of applying for a visa, again make sure that you give yourself enough time for this. You can obtain a visa at the airport in Kathmandu, but I don't advise this as the regulations and requirements may change, anyway you don't want to waste time at the airport do you?
Take most of your money in Travellers Cheques, US dollars are the most acceptable, pounds sterling and other European currencies are also acceptable. You will have no difficulty changing travellers cheques in Kathmandu and the main towns, e.g., Patan, Bhaktapur, Pokhara and Namche Bazaar. Make sure that you have changed enough money for your trek before you start off on the trail. When you cash in a travellers cheque make sure that you are given some small denomination notes, you will need these for refreshments along the trail. You should ensure that you are given a receipt each time you change money.