Since festivals provide us with a lot of photographic opportunities, ranging from wide angle to telephoto perspectives, hence, it is always wise to carry two cameras with two different (wide and telephoto) lenses. However, it is not a necessary condition but its always better to carry two for safety.
It is always useful to use continuous shooting mode along with AI Focus as it will help you to capture moving subjects and candid shots. Even try shoot in Aperture priority mode as it could help to get the DOF according to your choice and composition.
When you have planned shoot a festival, always try to do some prior research before going to the place, be it from guide books or internet. You should have an idea about the main auspicious aspects and the events to happen during the festival. Search in the internet for photos of the place and the festival already taken by other photographers.
Always prefer to shoot during the ‘magic hours’. Keep a check on the time of Sunset and Sunrise of the next day which would help you to get some perfect shots during those hours.
Even if you go to shoot as a group, try to shoot alone; otherwise it is not only very difficult to get original shots, sometimes you subjects may get confused and nervous too if they faces too many photographers. If you go as a member of a workshop, try to find a different POV and angle from your team members.
If you are new in a country and place, there is a big chance that you may get carried away by the people, Have a look, what is going on around and then start to shoot. Also, since you won’t have much chance for staged shots, so the shot and composition has to be planned very quickly. Hence, train yourself to quickly measure the direction of the light and shadows; interesting POVs, the aperture and shutter speed. Use your prior research to capture important religious aspects of the festivals.
It is very difficult to get a clear background in the festivals, hence you must compose in such a way so that background enhances your shots, you may include people bathing or praying; Sunrise or Sunset etc. in the BG while keeping your main subject in the FG, it makes your shots more relevant giving a feel of the place.