You're describing a difficult condition for any camera - action/movement in low lighting conditions.
First, if you're using your flash, turn it off. Unless you're on the field right in the middle of the action, you're too far away for the flash to be effective. Having it on will only confuse the camera.
Now let's talk about the three settings in your camera that impact how it deals with different lighting conditions. The first is the aperture, which determines how wide the shutter opens. The lower the f-stop number, the wider the aperture and the more light will come in. The second setting is the shutter speed. The longer the exposure, the more time light has to come in, and the more detail you'll get in darker areas of the photo. The third setting is the ISO. This setting determines how sensitive the sensor is to light. The higher the ISO, the more sensitive the camera is to capturing low-lit subjects.
The trick is finding the right balance between these settings for the specific conditions you're shooting in.
When there's motion in the scene, especially if it's fast motion, you need to keep your shutter speed fast enough to avoid blur. A fast shutter speed will "capture action" without blur. Unfortunately, a fast shutter speed isn't friendly to shooting in low light. So the trick is to have a fast enough shutter speed to avoid blur, but slow enough to provide enough light to work with the aperture and ISO settings you've selected.
The aperture setting is limited by the design of the lens. This is a case where
a better camera makes a big difference. Your camera has the ability to go to f2.8 when at the max wide angle. (That's pretty good.) As you zoom in, though, it goes down to f5.7 at the maximum zoom. That means the more you zoom, the lower the amount of light that can get in. Keeping the camera back at the full wide angle will improve your low-light shots. One of the things that the aperture setting effects is the depth of field. With a very low f-stop, there will be a narrow depth of field (less of the photo will be in focus). Things that are closer to the camera than your focal point and things that are farther away than your focal point will be out of focus. With a higher f-stop, more of the picture will be in focus.
Increasing the ISO allows your camera to "see better" in lower light, but has the adverse effect of adding noise (static) to the photographs. This is another area where a better camera has an advantage. The better the sensor, the less noise at higher ISOs. So the trick here is to have a fast enough ISO to work with the shutter speed and aperture settings, yet low enough to minimize the noise. Your camera has the ability to go as high as ISO 3200.
Here's a link to your camera's user manual.
http://gdlp01.c-wss.com/gds/7/0300001567/01/PSSX10IS_CUG_EN.pdf Check out page 84 for instructions on changing the ISO. Start at 1600 and see what that gives you.
After picking an ISO, there are two modes you can play with. The first is Av (aperture priority mode), which allows you to set how wide open you want the aperture. The camera will determine the optimal shutter speed. Try setting the aperture value bar as far to the left as it goes and try a few shots. Page 102 in the manual applies.
The second is Tv (shutter priority mode), which allows you to set the shutter speed and have the camera pick the optimal aperture. (Why's the abbreviation for shutter priority mode "Tv" on the dial? It stands for "Time Value."). Pick the slowest speed you can that doesn't result in blur. This will require some experimentation. Page 100 provides the details in your manual.
Now, if you've been shooting in full auto mode, your camera should have been finding some of these same settings. If you've been getting dark or blurry photos in auto, chances are you're not going to see a major change in Tv or Av. You may be able to refine the balance between darkness/blurriness and find a better balance than the auto settings were able to find, though.
If you still can't get the results you want, there's one other thing to try. You can force your camera to go into an even higher ISO mode by setting the ISO 3200 scene. Check out pages 95-97 in the manual. Set the dial to "SCN" mode, then select "ISO 3200" from the scene list. You're going to get a lot of noise at this setting, but depending on what you're looking to do with the pictures, it may work for you.
