The Sit Command is probably the most important thing that you can teach your dog or cat.  Yes, you can teach a cat to sit on command.  The sit command is also the easiest command to teach.
When you teach your dog to sit on command, you are also teaching them that it is time to be respectful and wait for instructions.  Having your dog sit is one of the best ways to make him calm down when he is being too rowdy.  Most dogs can learn to sit in just a few lessons.

1.  Stand facing your dog as he stands facing you.  Hold a treat in front of his face and wait until he begins to use his nose to sniff.  
2.  Once he is focused on the treat, say "sit" while moving the treat in an upward direction over his face.  His nose will follow the treat up and his rear end will automatically go down.  The moment his bottom touches the ground, reward him with the treat and praise.

Practice the sit command for about 15 minutes at a time.  It is important to do all dog training lessons in short intervals so you don't overwhelm your dog.  Remember, you want it to be fun and rewarding.  Once your dog has mastered 'sit,' then you can move on to 'stay' and the more complicated commands.  Good luck and Happy Training!

FOR CATS:  You can use the same method to teach your cat to sit.  If your cat does not go for treats, try some boiled chicken pieces or tuna flakes.
Another method is to place your cat on stool with a small seat.  Gently push down on her rear end while saying 'sit.'  If she doesn't put her rear end down quickly, move a bit closer to her and try again.  She will have to lift her head higher to see you and her rear will autimatically go down.  Again, the moment her rump hits the seat, praise, praise, praise!

Disclaimer
Please consult the services of a Professional Dog Trainer, Behaviorist or Veterinarian before implementing any of the advice contained on this site.