I am a photographer and although I have done it for a while I still need help capturing that right picture. Currently I have been taking photos at my church, I am having trouble capturing the spiritual dancers while their dance, or the church goers as they are praising. I know in order to capture a fast moving subject you have the set the shutter speed up a bigger number, but no matter where I set it too, the picture always comes out blurry. What is the best shutter speed to set to capture a fast moving subject?
I think your issue here is two-fold. You're not just trying to capture fast action, you're trying to capture fast action in low light.
There is no hard-and-fast set number that will guarantee you won't have any motion blur from fast action. The faster the action, the faster your shutter speed needs to be to "freeze" it.
The problem that's probably happening is that indoors, in a church, your light levels are low enough that even with a high ISO setting and your lens's maximum aperture setting, you still need a slower shutter speed to get a good exposure.
To get faster shutter speeds, you can only do a few things, if you're already maxed out on iso and aperture.
You can get a faster lens. Many consumer-grade lenses max out at f/5.6. This isn't particularly wide, and is called a "slow" lens, because of the shutter speeds it may force you to use. Getting an f/2.8 (or smaller f-number) lens gets you 4x or more light than an f/5.6 lens, if used wide open. However, faster lenses are more expensive (although primes can cut that cost down), and larger aperture settings make focus harder (thinner depth of field makes a much smaller target you have to hit), and the wider open a lens goes, the more flaws you can see in image quality (softness, chromatic aberration, vignetting, etc.)
You can add a flash. You need more light. Add more light. There are many ways to use a flash so that it doesn't give you that deer-in-the-headlights white look most non-flash shooters associate with flash. Bouncing is one go-to-technique. Going off-camera-flash is another.
You can fake a higher ISO setting. But I wouldn't recommend doing this, unless your camera maxes out around 1600 or 3200. It adds a crap ton of noise. But shoot RAW, and underexpose, then in post, push the exposure back up (i.e., push processing). This is what the "extended" ISO settings in most cameras do.
Use the blur creatively. Blur indicates movement. Sometimes that can be a good thing. Just make sure that the blur you're getting is from the subject movement, not from camera movement from handholding. The basic rule of thumb with camera shake blur is that your shutter speed needs to be at least 1/focal_length. Some folks also throw in crop factor. So, say, if you're using a 55-200 lens @200mm on a crop body, that would mean using a shutter speed of 1/300s or faster just to eliminate camera shake blur. If you've got good handholding technique.
See also: Why are my photos not crisp?
You are too short on your description. But here are the basic options.
A) Is the background also blured? Use a tripod.
B) Use a flash. Try to bounce it on the church celling to achive a more natural look.
C) Push the ISO... there is a chance your camera simply can not handle the situation. This in my opinion is the best reason to upgrade a camera, better low light response. What is your maximum ISO? If you have a maximum of 1600 you are in trouble, so go for the flash option.
D) Get a faster lens. And probably this is one good reason to upgrade a lens, a faster one. A 50 mm f1.8 lens?
E) Underexpose a bit. Shoot in raw and underexpose one or 2 stops. Yes you will have more noise, but noise is easier to correct than motion blur.
What is the best shutter speed to set to capture a fast moving subject?
The specific answer depends on the subject. Here is an insane camera... Photographing a beam of light... Yes you readed well: https://www.ted.com/talks/ramesh_raskar_a_camera_that_takes_one_trillion_frames_per_second? In that case they shoot video at a trillion frames per second... So that totally depends on the subject.
A talking person, a dancer, a racing car, a bullet... light.
I would say to shoot a preacher or dancer, arround 1/500 - 1/1000, but again, depends on the dance.
It depends on the speed of the movement, the distance and the focal length used. The moving subject will move at some angular velocity relative to your vantage point (this is given by the speed of the movement divided by the distance), your focal length determines the field of view, so you then know how fast the movement is relative to the size of your image sensor, and then you can convert that to pixels per second. The exposure time needs to be chosen such that the motion will be less than one pixel.
Since there are quite a few unknowns here, it's best to study some of your previous blurred pictures and measure the blur in pixels. You can consider an edge that should have been a high contrast edge that in your picture is smeared out over a number of pixels. Suppose that you took that picture at 1/500 seconds exposure time at 100 mm focal length and you measure the blur to be 7 pixels. If the next time you are at approximately the same distance, then using 50 mm focal length will get you to about 3 or 4 pixels blur. If you don't what to use use an even lower focal length, the remaining factor of 4 has to be obtained by using a faster shutter speed, you need a shutter speed of 1/2000 seconds. The ISO should then be increased by a factor of 4, if you use the same aperture.
Now, as Micheal Clark points out in the comments, if you choose to use a resized picture then the blur in the original picture can be larger. In that case you can go through this procedure where you use the blur size in pixels after you resize the picture.