Are you allergic to animals? Brush your pet out of doors, or ask someone else to do it for you.
The animal should be wiped down daily with a damp towel, and its living quarters or box thoroughly cleaned. If you must do these things yourself, wear a dust mask and wash your hands after you have finished.
Make your bedroom a pet-free sanctuary. You might also consider having an air filter installed in there.
Don't keep a cat's litter box in your bathroom (urine contains allergens), and if possible put the litter tray into a hooded box.
If your allergy to cats or dogs gets the better of you but you can't live without a pet, consider a bird, fish in a tank or a bowl, or a terrarium with frogs, toads, lizards or snakes.