The primary goal of the New Horizons Pluto-Kuiper Belt mission is to explore Pluto by 2020, before Pluto's atmosphere collapses as predicted by scientists, and then explore the Kuiper Belt objects in an extended mission. The baseline mission plans to launch in January 2006, using a Jupiter gravity assist trajectory to reach Pluto. The New Horizons spacecraft will arrive at Pluto as early as 2015, depending on the launch vehicle. For such a mission, whose exploration takes place during a brief flyby period after a long cruise, a thorough planning of the encounter is especially critical to the realization of optimal science observations. A detailed Pluto encounter trajectory design that achieves both solar occultation and Earth occultation by both Pluto and Charon is described in this paper, along with discussions of the design rationale and considerations. Science observations and measurements planned for the Pluto-Charon encounter are simulated and analyzed, and a comprehensive Pluto-Charon encounter process filled with detailed science observation simulations is demonstrated in a 3-D animation.