They are probably doing this the same way they did for the Atlanta Olympics. Military personnel from AD, Guard and Reserve Units will most likely be handling support functions, like medical support, traffic control, surveillance of Olympic facilites and general security and will not be armed. They may run some security functions, like screening points or roving patrols, that would require duties close to what LE does, but probably will not have any arrest or search authority unless under the direct supervision of an LEO. This would not apply to the Utah guard, however, unless they have been federalized for the event.
To handle the "armed" portions, the State of Utah has been actively recruiting (pre-9/11) LEOs and LE Agencies to send individual officers or teams of officers to Utah to assist. If I remember correctly, the LEOs bring their own weapons, and will be paid by the Olympic committee. All will go through a training program and be provided with uniforms and housing by the Olympic folks.