Welcome aboard. Yes, you're going to be told to read the manual. But read it to learn how to set your settings in either Av or Tv or M modes. Put your 55-300 on the camera and practice in a darker room or at dusk or at sunrise, etc, to try and simulate the lighting conditions.
With the Kx you should easily be able to go to ISO1600 and get some relatively clean shots. Leave it there. Set your aperture to about f8, and leave it there. This of course would be Av mode where you can let the camera choose the shutter speed. If those settings don't work for you try setting the camera for Tv mode, same ISO (1600), and set your shutter speed to about 1/200 (or faster).
What I'm really suggesting here is that you give yourself a crash course on exposure. 3 factors affect it, Shutter speed, Aperture, and ISO (or film speed). Fix one (in M mode) or 2 (in Av or Tv) and learn what happens to the others in various conditions.
If you show us some of the terrible pictures, with EXIF (exposure information) in tact, we may be able to help you further.
One thing that is useful to remember, the exposure for 30 feet will not be the same as the exposure for 100 feet. Each f stop (f8 to f5.6 for example) change, lets in twice as much light. Light can be thought of by an Inverse Square rule which basically tells us that if we have X amount of light at a given distance, without changing the light source, we will have 1/4 as much light at twice the distance. So if at 30 feet you get a good exposure with ISO 1600, f8, 1/250 for instance, to get the same exposure at 60 feet, you'll have to go to 1/60 sec to keep the f8 and ISO 1600. (1/250 / 2 = 1/125 and half'd again is 1/60 sec). Or, you will need to bump your ISO to 6400 to keep the same shutter speed and aperture. Get the picture?
Applying this to the idea you are shooting a moving subject, you probably want to keep your shutter speeds a little higher.