If you have made your own way to Tokyo from the airport, then getting to Hakuba should hold no fear. It comes down to either an express bus or public trains, the quickest method (bullet train & bus combination) taking just 3 hrs, but a direct express bus will be the cheapest. Depending on how much other travel you will be doing in Japan you may want to consider getting a Japan Rail pass (need to get it before you arrive in Japan and you can get a discounted one here).
There is only 1 direct bus to Hakuba a day, and that leaves at 07.30 am from Shinjuku station in Tokyo. If you can get that great, if not then you will need to change trains a number of times, and it will take you much longer than either the express bus or bullet train options. Make sure you get a Japan Rail passbefore you come.