I need to run water to my shop near my house to my utility sink for dog grooming what its the easiest and cheapest way to do this will I have any drainage issues as well
I have seen many situations where "summer" sinks have been created by running water lines to outbuildings. These are called summer sinks because since those outbuildings are not heated, they have to be shut down in the winter. If the sink is only used temporailty, you may be able to get away with this, oer somthing like a garden sink shown here: http://www.generalsuperstore.com/images/outdoorsink.JPG.
If you are runing a grooming business, you need a more permanent solution. Therefore, you'd need to extend your homes water supply and waste lines to the shop area. How this gets done has a lot to do with where they are in the building. Most likely, a new water supply line will be extended (after the meter) from the house to the shop (with it's own shut off valve for emergencies), and a new drain line will be run from the shop into to meet the home's waste line outside.