The Suwa region in Southern Nagano Prefecture is easily accessible from Tokyo and Nagoya.
Japanese train info can be found at http://www.hyperdia.com/en/
A taxi shuttle service is also available from Haneda, Narita, and Chūbu Centrair International Airports right to your accommodation. Despite the website, in practice English is spotty at best.
There are also bus services from Tokyo’s Shinjuku, Nagoya, and Osaka. Again, English will be hit or miss.
Driving is an option, but you won’t be able to get anywhere near the festival. Strict and varied traffic and parking regulations will be enforced, “official” parking will be expensive, and you’ll end up crammed onto shuttle busses with a gazillion spectators.
All to say, we recommend leaving your car behind and taking the train.