Studying charge transport through single molecules tethered between two metal electrodes is of fundamental importance in molecular electronics. Over the years, a variety of methods have been developed in attempts of performing such measurements. However, the limitation of these techniques is still one of the factors that prohibit one from gaining a thorough understanding of single molecule junctions. Firstly, the time resolution of experiments is typically limited to milli to microseconds, while molecular dynamics simulations are carried out on the time scale of pico to nanoseconds. A huge gap therefore persists between the theory and the experiments. This thesis demonstrates a nanosecond scale measurement of the gold atomic contact breakdown process. A combined setup of DC and AC circuits is employed, where the AC circuit reveals interesting observations in nanosecond scale not previously seen using conventional DC circuits. The breakdown time of gold atomic contacts is determined to be faster than 0.1 ns and subtle atomic events are observed within nanoseconds. Furthermore, a new method based on the scanning tunneling microscope break junction (STM-BJ) technique is developed to rapidly record thousands of I-V curves from repeatedly formed single molecule junctions. 2-dimensional I-V and conductance-voltage (G-V) histograms constructed using the acquired data allow for more meaningful statistical analysis to single molecule I-V characteristics. The bias voltage adds an additional dimension to the conventional single molecule conductance measurement. This method also allows one to perform transition voltage spectra (TVS) for individual junctions and to study the correlation between the conductance and the tunneling barrier height. The variation of measured conductance values is found to be primarily determined by the poorly defined contact geometry between the molecule and metal electrodes, rather than the tunnel barrier height. In addition, the rapid I-V technique is also found useful in studying thermoelectric effect in single molecule junctions. When applying a temperature gradient between the STM tip and substrate in air, the offset current at zero bias in the I-V characteristics is a measure of thermoelectric current. The rapid I-V technique allows for statistical analysis of such offset current at different temperature gradients and thus the Seebeck coefficient of single molecule junctions is measured. Combining with single molecule TVS, the Seebeck coefficient is also found to be a measure of tunnel barrier height.