-Get the shape file and load it into ArcGIS using the "Add Data" button. You could also drag it in from Windows Explorer/Arc Catalog
-If your data is in a geographic projection, you should get a coordinate readout along the bottom which is in geographics. If your data is in something else, right click on your dataframe in the Table of Contents (it will just be called "Layers"). Choose "Properties" and then the "General" tab. There should be a drop down menu for display units. Choose DMS (or whatever it is you want).
-If ArcGIS can't project your data it will let you know, but you seem to have projection files there, given the extention list you gave.
LMK how it turns out.
Edit: I should note that you don't *have* to reproject it just to get the coordinate readout in a different set of units. If you do need to reproject it,
-Open ArcToolBox (the red toolbox thing)
-Search for "project"
-Click on the "Project" tool
-Fill out the appropriate fields
Like I said, you shouldn't have to reproject it just to get a coordinate readout.