Your pets can be taught what they should and shouldn't do.
Praise and scold
If your pet does something it can be praised or scolded for, an icon will appear on the little photo of them at the side of the screen. This icon is a curved arrow. Click on the pet, and then select whether to scold or praise them. And to check you got it right, you need to click on what to scold or praise them for. There is only ever one option here. Then your sim will go to them (or they might come to your sim) and they will praise or scold them. Praising makes the cat or dog think that hwatever it just did was a good thing, and therefore the metre will raise is it was really a good thing. If it was a bad thing, then the metre will turn red.
If your pet is taught to be good, your sims will soon no longer need worry about the new couch being ripped to pieces or puddles greating them when they go into the kitchen.
Commanding
Once your cat or dog has filled a behavior metre, they can be commanded to do what they have learnt. E.g. you can tell your pet to go to bed, and if it has been taught to use a pet bed it will use that or sleep on the floor, but if it has been taught that it is alloud to sleep on a sim bed, it will resort to that instead.
Behaviors
Here are the behaviors which you can teach your pet.
Eats pet/sim food
If you catch fluffy the cat eating last nights leftovers which you carelessy left lying around, scold him and make him eat from his pet bowl instead. Either that or tell him that eating food made for sims is OK, and then end up with less food to eat yourself.
Uses a pet/sim bed
If your dog is sleeping on the bed and you want to keep your sheets clean, scold him and tell him to get off. Or praise him and have a warm comanion next to you in bed... providing your bed isn't single.
Just note that praising or scolding for 'staying off sim beds' will teach your pet whether to use a pet bed, whereas praising or scolding for 'being in the pet bed' teaches your pet whether to be on the sim furnature.