On Shinkansen trains and JR tokkyū (limited express) and kyūkō (express) services, there’s a choice of ordinary, or futsū-sha (普通車), carriages or more expensive first-class Green Car, or guriin-sha (グリーン車), carriages where seats are two abreast either side of the aisle (as opposed to three). There may be a choice between smoking, or kitsuen (喫煙), and non-smoking, or kin’en (禁煙), cars; all JR East Shinkansen services are entirely non-smoking. On Nozomi Shinkansen it’s also possible to buy standing-only tickets for a small discount.
Each train also has both reserved, or shitei-seki (指定席), and unreserved, or jiyū-seki (自由席), sections. Seat reservations cost between ¥300 and ¥500, depending on the season; they are free if you have a rail pass. You cannot sit in the reserved section of a train without a reservation, even if it’s empty and the unreserved section full, although you can buy a reservation ticket from the train conductor.
If you don’t have a reservation, aim to get to the station with thirty minutes to spare, locate your platform and stand in line at the marked section for the unreserved carriages; ask the platform attendants for jiyū-seki, and they’ll point the way. If you have a reservation, platform signs will also direct you where to stand, so that you’re beside the right door when the train pulls in.