Finding or taking good photos can be a lot of fun and very easy.  There are just a few things to keep in mind. 

1.  Work when your subject is relaxed and happy.  You want a natural expression.  Try to capture a typical expression or moment. Have someone there to help distract your subject as pets and children usually do not like to sit still. Again, I suggest taking a photo when they are doing something they love with a toy, game, etc.

2.  Take photographs at eye level.  Have someone hold your pet, if you need to,  and try to distract him or her from licking the camera lens. Make sure the image is in focus, so I can see the detail.

3.  Try to get in close and fill the whole frame with your pet or child, then take extra shots for the scenery and to capture each face.  Take as many shots as you can, I find I get only one out of 30 that are really useable. Take as many angles and extra shots as you can as it is hard for me to tell what the feet are doing if they fall in a dark shadow.  My final portraits are often pieced together from several photos in order to get a good expression on each subject in the painting.

4.  Natural daylight falling on the subject's face is best and provides the most accurate color and details.  However, flash is acceptable as long as the photo is clear and accurate.