There's frequent train service between the cities. Purchase your ticket at the time of travel.
There is no need to book in advance, unless you're traveling in the peak season. www.hyperdia.com for schedules and fares throughout Japan.
I’ll be going to Kyoto from Tokyo next week, on a Saturday. I haven’t decided what time I’ll be going yet. Should I be reserving my ticket? Or should I just show up the day of and buy it then?Can I buy a ticket online or should I be going to Tokyo station to purchase it? If Tokyo station, do I buy from a service counter or do I use a machine?By the way, I don't have a JR Pass.