How to set up XY Coordinate System

For Shape File:

1. Use ArcCatalog
2. Open the file (shape), connecting the Folder if there is not yet connected.
3. Right Click on Shape File name in TOC and Choose "Properties"
4. Click Select Button
5. Choose Coordinate System,

example : Coordinate Systems > Geographic Coordinate Systems >North America >

NAD 1983 (CRS)

another source :

ESRI WEB HELP

ESRI Froum