The best and most common place to install a dishwasher is next to the kitchen sink where there is access to both water and a waste line. If you don't already have a dishwasher, you probably will have to reconfigure your cabinets so that you can slide the dishwasher under the counter. Replacing a broken dishwasher is easier; they all have virtually the same dimensions, so you probably can just slide the old one out and slide the new one in.
A self-tapping valve, also known as a saddle valve, allows you to use an existing copper water pipe for other purposes without cutting or welding the pipe. The valve fits completely around the pipe; tightening the valve forces the tap, or pointed part that goes into the pipe, through the side of the copper pipe, which creates a puncture. A handle on the valve controls the water coming out of the puncture into the valve.
Because of the ease of self-tapping valves, you can use them to install dishwashers, ice makers, air conditioners and many other smaller appliances. They only work on copper pipes, however. After you connect the valve to the pipe, run a line -- normally plastic -- from the valve to the dishwasher intake valve. Some dishwashers require two self-tapping valves, one for the cold water and one for hot.
Vibrations from the various appliances in the kitchen and from the water rushing through the pipes can sometimes work loose the screws holding the self-tapping valve onto the pipe. If the valve loosens sufficiently, it can cause a leak in that area. It can take years to notice a small leak under the sink, so check any self-tapping valve every six months or so to avoid water damage.