It's always been tricky to me how to take a far distance picture(moving) in a low light situation. I don't think flashlight would help in this case since it can't reach to the moving object. For instance, I went to the water festival last time, trying to take boat racing at the evening which didn't have enough light to capture all the details. If I increase the ISO, it would get so much noise then the image quality would become crappy. Is there any ways or equipments that I can manage to overcome this problem?
Sometimes there is no substitute for speed. To capture a moving subject in low light you need a fast lens. Even then you need a camera that can take decent images at relatively high ISO. And you still will have to learn to pan with your subject so that it occupies the same spot in your viewfinder as it moves.
The shot above was captured with a Canon 7D + EF 70-200mm f/2.8 L IS II lens mounted on a monopod. Image Stabilization was set to mode 2, which helped smooth out my pan horizontally. ISO 6400, f/2.8, 1/60 sec. The original 5184x3456 pixel image was cropped to 3565x2377 px before being resized to 1536x1024 for web use. The plane was probably traveling about 250-300 mph which means in the 1/60 sec exposure time it traveled about 6-8 feet. I managed to pan my camera and lens at the same rate from about 1/2 mile away. Over the course of a seven minute performance I took 150 exposures, of which about 40 were good enough to edit, and another 15-20 that where good but of the same basic shot as another I chose to edit. I also spent a lot of time in post production dealing with noise reduction.
Two options, one is to attempt a tracking shot where you use a longer exposure and follow the object to keep it in the same spot. These kinds of shots are very difficult to pull off and require lots of practice. A tripod is also highly useful, particularly if the exposure is forced to be fairly long.
The second is to get better low light equipment, either a camera with better high ISO performance or faster lenses that allow more light in to the camera.
Up to 200 feet or so, high powered flashes can do the job as well, but once you get beyond that kind of range, it's going to rapidly become very limited what can be done by portable artificial lights. If you are able to coordinate with the subject being photographed, using a remote controlled flash that is near the subject can also be an option. There are some remote triggers (expensive though they may be) that can reach up to 330 feet. With the boat example, putting a flash on the boat and hooking it to the trigger could allow for the subject to be lit locally and photographed from a distance, but this isn't an option in many situations.