Tohoku Shinkansen superexpress train connects Tokyo Station and Sendai Station. It costs about 10000 yen or more depending on the day and seat type (non-reserved, reserved, green-comfort). The travel time is about 1 hour and 40 minutes for a Hayate train, and 2 hours or more for a Yamabiko train. Avoid a Max Yamabiko (different from Yamabiko) unless you want to enjoy a double-decker train for ages.
A ticket can be either for a reserved seat or for a non-reserved seat. With a non-reserved ticket, you can take any non-reserved seat on any train any time while the ticket is valid. With a reserved ticket, you should take the specified seat on the specified train. However, should you miss the train, you can still get on a later train and take a non-reserved seat. No non-reserved seat is available on a Hayate.
Narita Express takes about 60 minutes from Narita Airport to Tokyo Station. The regular fare is 2940 (+-200) yen. (It costs less if you purchase a JR ticket directly through Sendai than buying two separate tickets.) A rapid train is also available at a lower fare of 1280 yens. It takes about 84 minutes.
At Tokyo Station, catch a Tohoku Shinkansen train.
Skyliner on Keisei Line connects Narita Airport and Keisei Ueno Station. It costs 2400 yen and takes about 45 minutes. A limited express train takes 71 minutes and costs 1000 yen.
After getting off at Keisei Ueno Station, walk to JR Ueno Station and catch a Tohoku Shinkansen train. Virtually every Tohoku Shinkansen train stops there. Note that JR Ueno Station is not a commencing station. Therefore, if you buy a non-reserved ticket, it sometimes happens that all non-reserved seats in a train are already occupied, and you may have to stand up in a car or wait for the next train.