A tip often cited by pro pet photographers to get interesting pictures of dogs is to get down to the dog's eye level. I agree. This is because most pet photos are taken looking down at the pet. And you'd like to take a picture with the idea of "this is what I see", and not take a picture that looks like everyone else's.
If you go to greyhound events like the Solvang Greyhound Gathering, Greyhounds In Gettysburg, and Greyhounds Reach the Beach at Dewey Beach, you might see some dude occasionally photographing greyhounds by walking in front of the dog, keeping pace with it, and hunched over while holding a camera down at arm's-length, pointing it at the dog, and snapping pictures. Ummm...that would probably be me.
I would not be surprised if I amuse more people in this manner. I'm sure one of my friends has a picture or two of me doing this. But I like the different perspective from shooting this way. For example, this is Abbey, one of the greyhounds I took pictures of at Dewey:
I used a wide-angle lens to make sure the dog is in the field of view since I can't look through the viewfinder to see the dog (in this case, I'm using the 18-200mm zoom set at 18mm). I aimed the camera in the general direction of the greyhound, set the autofocus mode to "Auto Area AF" (the solid white rectangle icon on the back of the D300), and the focus mode to Continuous-servo AF (also known as AF-C) since the distance between me and the subject is always changing. Then I take a few shots and see what I get. Since wide-angle lenses have great depth-of-field pretty much everything is more or less in focus. But it also overly exaggerates the size of the nose compared to, say, the back legs.
Since I was in broad daylight I used my SB-800 flash to fill the shadows somewhat, and set the flash mode to slow-sync so that the foreground and background would be properly exposed.
(Shot with the Nikon D300 using the 18-200mm zoom lens set at 18mm; shutter-priority mode with shutter speed set at 1/500 second and ISO 200; camera chose aperture of f/10; SB-800 used for fill-flash; flash mode set to SLOW; auto white balance; processed in Lightroom; shot in RAW.)