Use your best camera. Most smart phones these days are great for capturing details.
Take your time and relax. Animals pick up on our moods, and you want him looking his best.
Go outside. Natural lighting is best. Avoid bright sun/shadows. Dawn and dusk gives you the best light.
Get down to your pets level or lower. You’ll get a better shot than shooting them from above.
If you can see the details clearly when you enlarge on your phone, the I’ll be able to see them too!
Here are some of my reference photos