Hi Jerry,
Well firstly you don't want to use the camera's flash, because (a) you might startle the dogs and (b) be told to stop taking photographs or thrown out. So you'll need to set the ISO quite high to make the camera's sensor more sensitive to the available light in the arena. (I'm presuming the event is being held indoors.) This should also enable your camera to use a faster shutter speed to freeze the action if the dogs are moving as you might need it as high as 1/500th of a second. To help with this select as wide an aperture as your camera lens will allow, say f/5.6, but you will have to watch your depth of field as this will be quite narrow if you've zoomed in close. I suppose you would like to isolate the dog and handler from what's in the background and you will get a nice blurry background with these settings.
Another technique you will find useful is panning. This is where you pan the camera to follow the movement of the dog in this case and press the shutter whilst continuing to pan the camera. You can use a 1/30th of a second shutter speed for this and the effect you'll get is a dog and handler frozen in time but the background will be blurred by the sideways movement of the camera giving an impression of movement in the shot. If you've not done any panning work before it's a good idea to have a practice beforehand as it takes a little bit of getting use to until you perfect it. Personally I always found as I pressed the shutter I stopped panning the camera and the whole image just ended up being blurry so that's why it's important to keep following the dog with the lens and keep it trained so the dog always stays in the same area of the frame as you take the shot.
Hopefully I haven't missed anything, but if there's anything else you need to know or just aren't sure about then just ask.