We have two dogs and two cats, and our son loves to interact with them, but his form of interacting is not particularly enjoyable to the animals...
Some of the things he does are just annoying, like picking up pieces of paper and putting it on the dogs. But at other times he pushes the animals off the backs of the sofa or counters, pulls their hair, and he loves to chase around the small dog who is afraid of him.
So how do I teach my son to play nicely with the animals?
I think just like you teach your dogs to play nice with other dogs or kids. I don't really see any other thing than just the generic methodology. Maybe you can spend some time with your child and the animals to show how it should be done.
If he/she already knows how it 'should be done' and is testing limits, be very clear about what is and what is not nice behavior around animals. Be very consistent about it. Make sure you explain why a behavior is unwanted, set a punishment and be sure to follow through with that punishment if the behavior continues. Afterwards, ask your child why it was punished and explain again.
As a final note: animals might even punish the child for its misbehavior. If that ever happens, try to make it a positive experience for the child by having the animal 'make up' to the child, for example by petting it together.
There is something that a teacher told me regarding the interaction between our toddler (3) and our infant (1 year). When the toddler does something to his baby sister that is not terrible but just not nice (like taking away a toy she is holding) you should talk to the toddler about how he hurt the offend-ed's feelings. Since the baby (and in your case animals) do not talk, they can't express their reaction with words.
It is important to try to explain to the toddler that his actions affected someone else in a wrong way. She stressed that small punishments (like timeouts or saying sorry) might not be effective because then kids might think that its OK to do the bad things as long as they say sorry afterward.
I have a 3-year old boy and 1.5-year old girl, and a (overall friendly) cat. As infants both kids were rough to the cat, with hair pulling and hitting, although each was different in what they did. Once they could walk, then chasing the cat was a fun activity. They have very little self control and get excited when the animal is around.
Each kid is different; the girl at 1.5 is a lot gentler with the cat than the boy was at the same age. In fact, she's about as gentle as he is at 3! I chalk that up to different natures.
Throughout this, we've done all the various things others have suggested, but I think the thing that helped most was just growing up and gaining maturity. Now that the boy is 3, he takes pleasure in seeing her sit on his lap while he pets her.
There have been a few cases where the cat didn't like something, and while we haven't had any scratches or bites (it's a very self-controlled cat), there were a few close calls. Those gave us opportunities to teach the boy about the cats claws and teeth and how she protects herself. He got (accidentally) poked by a claw once, and that seemed to wise him up quickly as to the consequences of scaring the cat.
At 3, the question of the day is always 'why?', so use it to your advantage. Why do we have pets? Why does the pet live here? Why does it chase mice (or cats)? etc. etc. Sit with the child and observe the animal quietly, and explain what it's doing, and why. And +1 to the other answer to role model how to handle the animal properly, and why.
I caught my one year and ten month old son, holding a stick and was about to hit the dog. I immediately took the stick away from him, and told him that it is bad to do it. At this age, my son knows what is bad already, so in a way, I was able to channel the information. I also try to show him how to take care of the pet, because toddlers often mimics what they saw in adult. When he sees that I care for the pet, he will slowly how to deal with them.
