This thesis discusses an experiment, which has demonstrated transverse laser cooling of a pulsed supersonic beam of strontium monofluoride (SrF) molecules. Producing ultracold molecules is important because they could advance many fields including many-body physics, quantum chemistry and precision measurements to explore fundamental forces in nature. Direct laser cooling of molecules is a new and promising way to produce molecules with temperatures in the sub-millikelvin range. In the experiment, SrF molecules produced from a pulsed supersonic source were cooled in the transverse direction using light from just two lasers. The molecular beam brightness was increased by about 20%. I discuss the detailed experimental setup, laser system and data analysis. I also present several theoretical models, which give insight into the cooling experiment. Finally, I discuss improvements to this experiment, which should enable higher yields of ultracold molecules to be produced.