To realize the various benefits brought by Low Earth Orbit (LEO) satellites in single-receiver high-precision GNSS-based Positioning Navigation and Timing (PNT) services, LEO satellite orbits and clocks need to be processed and delivered to users in real-time with precision of a few centimeters. While post-processing of cm-level LEO satellite orbits and clocks can be widely achieved, real-time processing faces various Challenges. When the number of LEO satellites increases, the observation data downlinked to the processing center may experience large and complicated discontinuities and incompleteness depending on the downlinking strategies. Even with the observations downlinked in real-time, the LEO satellite clock precision tends to be very sensitive to the continuity and quality of the GNSS real-time products. This study first introduces the procedure for ground-based cm-level real-time LEO satellite Precise Orbit Determination (POD), including near-real-time POD, short-term prediction, and ephemeris fitting/broadcasting. Next, the short-term predicted orbits and long-term predicted clocks of LEO satellites are introduced and properly constrained in filter-based real-time LEO satellite clock determination to achieve a precision of about 0.2 ns. Strategies to deal with sub-optimal observation data and GNSS products are explained. With the proposed methods, a Signal-In-Space Ranging Error at sub-dm to 1 dm can be achieved in practice.