Nikon D3100 Action shot photos?

I ride horses and at a competitions i have been wanting to take pictures but they are blurry. I got this camera so it would be easy to use. The Competitions are in a indoor arena. So on high shutter it is to dark even with the lightness on high. How can i make my pictures clear when of people going over the jumps thanks.
ps i have it on sports mode.

The following should fix your problems.

1. Get a fast lens (F2.8 or lower)
2. Set your camera to aperture priority (A) and use low F numbers (as low as your lens can)
3, Set your camera to high ISO as in 1600 or use AUTO ISO

If you can't use flash, and you have to have a high shutter speed, then the only other option is a wider aperture, which is probably going to mean a new lens.

There's a number of things you can try to do to help improve your photos. You might have the 18-55mm kit lens, which is a little slow honestly (because of the aperture of 3.5-5.6).

If you can, try a different lens. It will have to be an AF-S lens if you want autofocus. I highly recommend the 35mm f1.8 or the 50mm 1.8 AF-S lenses. Both are priced around $220.It's possible for you to trade your original lens to discount the price, but you'll lose zoom capability.

With those lenses, or with your zoom, try a few other things to help take faster shots.
-Take the camera and change the ISO to a higher number for some digital amplification to get faster shutter speeds. If you go too high, past ISO 1600, your shots will suffer from grainy noise. So you'll have to play with it a little.
-Setting the dial to A (or aperture) is good to change the f# lower. Or setting the dial to S (for shutter speed) can help you set the camera to faster speeds. But M (for manual) might be better to control your shutter speed and aperture too. Set the f# lower, but set the shutter speed faster. 100 is decent, but if there's movement, you'll have to make the number higher and higher (i.e. 200, 250, 300 etc). This affects the lighting in your pictures though and as the shutter speed gets higher, your images get darker.
-Figure out focus lock. When you are at a certain distance from the subject, set focus lock so that when they move your lens isn't confused on where to focus.

I have to say, the D3100 may be a little easier to use than other DSLRs, but to get the shot you're looking for, any camera takes a little experimenting. Especially DSLRs. You'll definitely want to try the different settings to understand what's the best for your needs before going to the next competition. Best of luck.