A high-efficiency gamma-ray counting system has been built at Los Alamos National Laboratory for use in analyzing nuclear forensics samples. This system consists of two clover high-purity germanium detectors and is surrounded by a thallium-doped sodium iodide annulus. Special precautions have been taken to ensure the system has a low background. The system is connected to XIA Pixie-4 fast digitizers and collects data in list-mode. This work is split into two main parts. The first part describes the proper steps and techniques to initialize the settings of a detector system connected to fast digitizers in order to optimize the system for resolution and throughput. The various counting modes for this particular system are described in detail, including the benefits and drawbacks of each mode. Steps are then shown to characterize the system by obtaining efficiency curves for various counting modes and sample geometries. Because of the close counting geometry involved with this system, true-coincidence summing factors must be calculated, and are done so in part by measuring the peak-to-total ratios of the system in its various counting modes across a wide energy range. The dead-time for the system can be complicated due to the multiple inputs of the system. Techniques for calculating the dead-time of multiple-detector systems are discussed. The second part of this work shows the system's usefulness in analyzing nuclear forensics samples, specifically irradiated enriched uranium. Three fission product parent-daughter pairs of different lifetimes are analyzed over a course of six months. The activities of each nuclide are calculated at each time step. Age dating techniques using the parent-daughter pairs are discussed, as well as the detection limits of each nuclide for a range of sample ages. Finally, avenues for further research are presented, as well as potential sources of error or uncertainty for this work. / text