Movie theater seats in Japan are reserved seats only, at the time of ticket purchase you will need to choose a specific seat. Some of the ways you can buy movie tickets in Japan is through online reservation, movie ticket kiosks and over movie theater ticket counters.
By experience, the most convenient way to buy a ticket is through an online reservation. I usually go to Toho Cinemas whenever I want to watch a movie. Toho Cinemas is the movie theater giant in Japan, it has several movie theaters all over Japan. At Toho Cinemas Shinjuku they have Godzilla on their side!
Here are the steps on how to buy movie tickets online for Toho Cinemas.