You're going to have to start using Aperture Priority, (AV).
What lens are you using?
For starters, since you haven't learned about aperture/shutter speeds yet, if you're shooting your dogs in a controlled environment, with plenty of light, try setting your camera to AV mode, set the aperture anywhere from f/5.6 to f/11, and if you can't reach a fast enough shutter speed, set up more lights, or use a tripod. If you're using flash, set the camera to Manual mode. Don't be scared of the "M."
You are holding a digital SLR, not a point and shoot. Most importantly, you don't have to develop any film. You have the freedom to experiment, and you should be able to learn very quickly by just playing around with different aperture and shutter speed combinations. Have fun!
T-1000