Black and white dogs are very difficult for a camera sensor to handle. (I would know!!!
) It depends somewhat on what kind of equipment you are using what your options are. The best result can be obtained with a DSLR with spot metering, and then use good image processing software, like PS Elements or Lightroom. (Photoshop works great too, but unless you're a photography fanatic, you probably don't want to spend the big bucks for it OR learn to use it... Both the other programs are less than $100 and relatively easy to learn)
If you have a DSLR, expose for the white, since, if you blow that out, you can't recover it) and then pull the details out of the dark in you processing software. You can do "spot" adjustments in both of these programs to pull detail out specifically in the eyes if you need to)
You can use a low power "fill flash", preferably off-camera, to get some like into their eyes indoors or out. Sometimes this actually looks best OUTDOORS, where the flash can't out compete the sunlight. If you have a P&S, the built-in flash is low enough powered that if you aren't too close, it can be useful too. If you need to tone down the one on a P&S, you can play around with taping a few layers of tissue paper over the flash until you get the effect you like. (You can do this with the built-in flash on a DSLR too)
Just as bright, indirect light is best indoors, bright overcast days are much better than strong sun shine outdoors. The overcast acts as a diffuser, and reduces the tonal range to something the camera sensor can handle. A small pop of flash can still add a nice catch light to the eye and make them "pop" more. Another EXCELLENT way to throw light into a dark face is to set the dog up facing a white wall... house, garage, etc. You shoot toward the dog (away from the white wall) allowing the wall to act like a big reflector, bouncing light into the dog's face. This photo of Kodi was taken exactly that way... no after capture adjustments were made to this other than a tiny bit of vibrance and clarity added. Actually, there is a TON more detail in the image than shows here on the forum... the forum, for some reason, makes all my images appear darker and not as sharp. If I am adjusting something specifically for the forum, I take this into consideration and lighten/sharpen it a but more. But in this case, I wanted to show you the file close to how it came out of the camera.