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.
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.
Here are the behaviors which you can teach your pet.
Your sims aren't likely to want a wild animal tearing about the house, so you need to teach your pets to be calm. Praise them for calmly watching TV or sniffing other pets calmly, but scold them for yowling, howling or running around crazily. Soon that wild animal will turn into a perfect calm pet for your sims.
This isn't so much an issue for cats as they clean themselves naturally. However, dogs, especially Pigpen ones will roll in all sorts of things, dig holes and lick puddles, no matter what the source is. You can stop this behaviour by praising dogs that don't try to escape their bath.
Eats Pet Food/Eats 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.
Gets on Sim Furniture/Stays off Sim Furniture
This behavior has no effect on whether your pet sleeps on a sim bed or not. Dogs will sometimes get onto the sofa to have a rest, and a cat may also find the kitchen counters comfortable. Scold them for doing this and praise them for 'relaxing' in their pet bed. Soon you'll have your setee all to yourself again.
Goes on Sim Beds/Stays off Sim Beds
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.
Cats will happily do their buisness in a litter tray if you provide them, so you must praise them for using that. However, with dogs you need to scold them for doing their buisness inside the house and praise them for going to the toilet outside. Of course, you still end up with puddles out in the front garden if they haven't decided to water the flowers. Cats can also be taught the command 'use toilet', which means that, if they have been taught to use a cat litter, they will use a sim toilet instead. This saves you money as you don't need to buy a litter tray, but the toilet will get clogged much more quickly!
Unles you want all the neighbours to fear your house, you need to scold your cats and dogs for hostility to others or for fighting. Praise them for playing nicely, and for asking to be petted. That is, unless you want to scare all the locals away!
It is vital that you praise your cats for using scratch posts and dogs for using chew toys if you don't want your furniture being destroyed. After all; a chew toy is a lot cheaper than a new sofa every day! Once this behavior is learnt, your pets will stick to playing with their toys rather than your living room.