You will need to merge your shapefiles and then build a new map from that.
For starters, you can move the data between different mxd's using drag-and-drop or by right-clicking>copy, then "Paste Layers".
Now, using ArcToolbox, search for a tool called "Merge" (I think it's in Data Management, but I'm not sure any more) and use this to merge the county-Shapes into a new State-shape.
Important: If the attribute tables of the county-shapse have identical field names, this will work well. If the field names don't match, you'll end up with empty fields and missing information, so you might want to check that first.
