Quite often an eye level portrait of an animal will be the most successful as in this image of Jasper by Robin:
Jasper
There are two or three ways (please feel free to add more if you have some) to attain an eye level view:
1. Get your camera down to the eye level of the dog. Of course this is easiest if you have a large dog who is standing. Otherwise it can be difficult to get down to the level of a small dog (especially when you are as old as I am). An articulating LCD can help if your camera is so equipped. If you don't have an articulating LCD, a right angle finder such as this would help - these are available on eBay both used and new. They are for specific cameras so ensure that the finder you buy is for or can be converted to fit your camera...
Another way to get down (for us old folks is to have some sort of stool to sit on. I often use a folding cane stool like this..
http://www.ebay.com/itm/FOLDING-PORT...sAAOSw0JpV5FpG
I have been also using this cane stool for events like auto sports and airshows
2. Get your dog up to the level you are comfortable with. This can be with the dog on a table or a chair. I had Carlie on a recliner chair with a fabric throw covering it. I was sitting on a roll-around office chair that way my camera was almost exactly at her eye level and I had the freedom to quickly adjust my shooting spot...
or it can be with the dog on a slope. The slope has advantages since, a slope with foliage such as ice plant makes a nice foreground and background for just about any color dog...
3. Finally (but this doesn't have to be final if someone else has additional ideas) shooting a dog from a long distance with a long focal length lens will narrow the angle between the dog and your lens and make it look like you are shooting from a lower angle that you are actually shooting. This was shot at 116mm on a 1.5x Canon DSLR (185mm equivalent)...