Try to use a camera with a high resolution (Usually anything over 1024x768 pixels is considered high resolution) this will ensure that I can see all the detail to make you a splendid portrait that you will be truly happy with!
Personally, I think the best photographs are taken outside. It gives a good, true light and helps to portray the subject’s natural colour/skin tone/fur. You also avoid the dreaded ‘red eye’ when you take photographs outside in daylight as there is no need for a flash.
Lots of natural light is great for black or really dark haired animals as the reflection of light on the coat helps to give the pet shape and form.
I realise it’s really tricky trying to get your animal (or child) to pose for a portrait, the two things that I would suggest are using food or toys to distract them or hold their attention whilst you take a quick snap.
Getting down to their eye level is quite important as taking a photograph looking down at them will give an awkward perspective.
Unfortunately I am no ‘David Bailey’ but learning from experience and some of the ‘not so good’ photos I have received, it really is worthwhile spending a bit of time getting a good shot.
The better the photo, the better the portrait!
On a number of occasions I have had to do portraits from pets that have deceased, in which case I try to make the best portrait possible from the photographs that you have.