To avoid the need for scripting and to do this quickly do the following: Open ArcMap and add the shapefile to a blank or existing map. Open the layer properties of the shapefile (double click the layer or right click the layer and choose properties), go to the Fields tab, turn off the visibility of all fields (the second button above the field list outlined in red below) and then turn on the visibility of just the fields you need by checking the box next to each field name.
At this point all the fields will be hidden in the tableview of the layer, which may be all you need if you don't really have to actually delete all of the fields, just hide them in a particular map.
To fully remove the fields right click the layer in the map's Table of Contents (the layer list) and choose Data-> Export Data..., set the output location and shapefile name, and press the OK button. This will copy the layer features to a new shapefile with just the fields you want.
ModelBuilder can do the same thing as the layer properties using the Make Feature Layer tool and its field list and all other tools that take a layer as input will respect the field list whether or not the tool that takes that input supports a field list.