Upon arriving at Tokyo Station, you need to buy a ticket for the Tohoku Shinkansen (bullet train) to Sendai. Tickets can be purchased at the ticket counter or at one of the ticket vending machines located near the wicket. The Tohoku Shinkansen generally consists of 12 or 16 cars, the first five of which are for people without seat reservations, and the remaining cars are for reserved seating. It will probably not be necessary to have a seat reservation, in which case the ticket costs 10,080 yen and you must sit in one of the first five cars (the first two cars are non-smoking). A ticket with a seat reservation costs 10,590 yen.
There are two different services on the Tohoku Shinkansen --the Yamabiko train, and the Aoba train. Both trains go to Sendai, but the Yamabiko train is a super-express train, which takes about 40 minutes less time, so this train is preferable. It leaves every 20 minutes or so, and the trip takes less than two hours.
Attention: As the Tohoku, Jyoetsu, Yamagata, and Akita Shinkansen all leave from tracks 22 or 23, please be careful not to get on the wrong train. The platform electronic indicator signs show the destination of each train in both Japanese and English. Some Yamabiko trains, with 17 cars, have a section with cars colored gunmetal grey. These grey cars, called the Tsubasa section, are not bound for Sendai (the train will separate into two parts before reaching Sendai), so please make sure you sit in one of the other cars.