It is recommended that the two cats be kept in different parts of the house for a day or two and then allow them to meet at feeding times when they are hungry and distracted from each other by the desire to eat.  Separate bowls, please!  Sometimes the cats will have a lot of disagreements, ranging from a lot of hissing and display behavior with no physical contact.  Violent combat is more common among un-neutered males, fertile females or mother cats with kittens.

Some cat simply ignore each other and make their own arrangements to share the living space, such as one having the kitchen, while the other takes the lounge.  In all interaction with cats, the owners must favor the "top cat" which, unless the cats eventually decide otherwise, will be the original resident cat.  Top cat should be fed first, petted first and definitely not be disciplined for hissing or swipping at the new cat.  In severe cases of aggression between the cats, the owners may try to deter attack by squirting the attacking cat with a water spray when it exhibits aggression.  However, this only works if the owner is present and has a quick trigger finger.  Veterinarians can sometimes assist in calming aggressive cats with either hormones or sedatives.

In most households with multiple cats, all the felines live happily and gain companionship from each other's presence in the owner's absence.