Buses from the Shinjuku long-distance bus station run about once an hour. The trip takes about 3-1/2 hours; fare is ¥4000 one-way or ¥7200 round-trip.  There is also a similar bus to Matsumoto here, it just goes via Kofu.
123bus is a company which provides daily bus services between Osaka and Nagano. With English online booking service.
There are many mountains in Nagano, so in winter there are many places to ski and do snowboarding. There are also many campsites and onsen, in easy to access locations.
Go see the Japanese Macaques in Jigokudani yaenkoen, you'll be able to get really near to them. Watch out as they can be a bit aggressive! Take the limited express metro to Yudanaka from Nagano, there'll be buses that take you there.
In culinary terms, Nagano is best known for its soba (buckwheat noodles), known as Shinano soba (信濃そば) or Shinshū soba (信州そば), with those from Togakushi considered by some the best in Japan. Miso (fermented bean paste), a staple of the Japanese diet is also a famous Nagano product. Among foods characteristic to the region are oyaki, small grilled doughballs filled with vegetables or meat, and on the unusual side, basashi (raw horse meat) and inago (locusts). There's also the Kamameshi bentō, a type of bento (Japanese home-packed meals), sold at train stations in Nagano prefecture. It is cooked and served in a clay pot. The pot is a souvenir item.
Apples are one of the special products of Nagano. The taste of Nagano apples is sweet and juicy. The yield of apples in Nagano is the second largest in Japan.