Practicing basic training as soon as your pet comes into your home is key to having a well-behaved dog or cat later on. Check with the animal shelter about local training classes and ask friends and family about pet trainers they trust.
For dogs, try practicing simple things like sit, stay, heel,come and down for about five minutes every day and reward him or her with love during the successes. You might find training a cat a little different than training a dog. You'll want to deter bad behavior such as scratching furniture without scaring him. Often, it’s as easy as interrupting the cat during the act. This can be done with a distracting noise like the tapping of a tabletop.
Also, depending on the age and previous life experience of the pet you may have to potty or litter box train the animal. Remember, accidents happen, so try to be forgiving and don't punish your pet. Instead, praise when he or she uses the litter box or goes outside to do his or her "business."