Patience is key to a successful introduction.  Do not try to introduce the new addition to the others as soon as you get it home.  A successful introduction may take only a few days, but can sometimes take a number of weeks.  Place it in a separate room with its own litter box, food and water.  If the cat is coming from another home, ask the owners if you can borrow or have an article the cat is familiar with or fond of such as blankets, pillows or sleeping baskets.  Place this in the room the cat will be confined in.  A stressed cat is more comfortable in a small space which it can quickly establish as safe.  Many cats will continue to return to this room whenever they are distressed or frightened, even years later.  Don’t choose the other cat's favourite room.  The cat should be kept confined for 2-4 days.  Watch your cat for changes in its response to the new cat.  When its attitude changes from irritated or surly to interested and curious, you can proceed.  
No matter how well you think things are going, confine the cat for at least 24 hours.  This is not being cruel to the new cat.  Territorial spraying and litter box problems are often the result of a rushed introduction. 

Do not let the cats see each other immediately.  They will be aware of each other's presence by scent.  Over a period of time (usually 2-4 days) they will become accustomed to the new scent, making the initial visual introduction less stressful.  Feed your cat(s) outside the room where the new cat is confined.  A string with sponge balls, or toy fur mice attached to each end, run under the door is a great way to establish contact without confrontation (remove the string when you are not home for safety).  The cats can tug back and forth and begin to play with one another. 

If you have a carrier it is wise to place the new cat in it for the initial introduction.  Place the carrier where your cat can view the new cat.  This allows them to safely observe each other.  Do not expect too much from the first meeting.  The cats may act in a hostile manner towards each other, spitting and growling.  If the meeting is going poorly, keep it brief and repeat meetings in this manner frequently over the next couple of days.  When the meetings are going well (cats seem less hostile or indifferent towards each other) remove the new cat from the carrier and place it on a large thick towel beside you, not on your lap.  If possible have someone there to shower your original cat with attention, distracting it with toys and play is often very helpful.  Repeat this step a number of times before allowing the new cat to venture off the sofa.  At this point, if the cats are tolerating each other well, simply supervise them.  If they react aggressively, break their eye contact by placing a newspaper before the more aggressive cat’s face.  You want to prevent a physical attack; generally at this stage the cats will have grown fairly tolerant of each other. 

Note: If you do not have a carrier be very cautious in handling the new cat.  Sit on the sofa and place the new cat beside you on a large, thick bath towel.  If things go badly you can wrap the towel about the cat and safely remove it from the room.  Do not allow the new cat to leave its position beside you.  If it becomes too restless return it to its room.  Repeat this many times before allowing the cat to venture off the sofa. 

Note:  Fights rarely happen, but it is wise to be prepared just in case.  Keep a large glass of cold water and a broom on hand in case a fight breaks out.  Dousing the cats with the water will usually break up a fight immediately; it is messy but it will save you from being injured trying to separate them yourself.  If one of the cats renews the attack, block it with the broom.  Retrieve the less riled of the cats (use the towel) and place it in a separate room.  Go back to the beginning and repeat all the procedures again.  Don’t give up, some cats simply take a little longer than others to make the adjustment. 

It is wise to provide separate litter boxes for the cats during the adjustment period.  It is easier to prevent litter box problems than to solve them once they have been created.  If your litter boxes are kept at the end of a narrow hall or at the base of a stairwell, continue to provide the new cat access to the litter box in the room it was initially confined in.  Some cats will ambush the new cat going to or leaving the litter box.  If this happens it could become reluctant to use the litter box. 

Note: After you have introduced a much younger cat (under 6 months) it is a good idea to separate it from the larger cats whenever you are not home.