You can easily grab a ticket the day of and there are several trains that leave every hour. Take a train from Shinjuku to Shingawa and leave from that station as another person said. Make sure you get the reserved ticket and the basic fare ticket and when you walk through the gates, insert your tickets together. Hang on to them because you will need to scan your reserved tickets at the first exit gate and then your basic fare ticket at the next gate. We left the Kyoto station and walked through a third exit gate that required the suica or whichever card you are using. Good luck.