Hønefoss is a town in the county of Buskerud.
Hønefoss, literally Hen-waterfall(commonly (mis)translated as the more catchy name "chickenfalls") is named after the waterfall in the middle of the town.
Trains pass through on their way to Bergen, Oslo and Drammen. About two hours travel time from Oslo. The train station is located just outside of town, within walking distance from the town centre. Just follow the foot-path downhill.
Buses leave every hour from Oslo Bussterminal, until late in the evening. Night-buses on the weekends. The trip takes around one and a half hours, and is worth it for the view alone. You will get a magnificent view over the great Tyrifjord Lake, one of Norway's biggest inland lakes. Make sure you get a seat on the left side of the bus when travelling from Oslo, to get the best view.
Askeladden reiser  has a regular transport from Hønefoss to Oslo airport Gardermoen  eight times every day from 05:30 in the morning to the last return from the airport at 10:45 in the evening, except for saturdays. Check the schedule under the link "Gardermobussen". 
The waterfall in the middle of town is not very impressing if you have seen a waterfall before. It might smell a bit odd since the river flows through a paperfactory not far from the city. But if you get the chance to see it on a sunny day when the dam is open it has it's charm. There is also a park nearby, Nordre park("The northern park"), where you can sit, relax and enjoy the view of the waterfall.
If you enjoy nature it is lot to see around Hønefoss. If you enjoy cross-country skiing or hikes, the forests around Ringkollen is a great place to go, both during winter and summer(although you may have a hard time skiing there in the summer). For downhill skiing and snowboarding, Norefjell is located 50 km northwest of Hønefoss. Buses goes to both Ringkollen and Norefjell from the central station in Hønefoss, but not too often so plan ahead.
As in all of Norway, there are few real budget accommodations available. The cheapest option is to simply camp out in one the many woodlands that surround the town. One such place, within short distance from the town centre, is in the Kartverk-forest. Take a bus from the centre to the stop "Kartverket" and simply walk into the forest from here.
During summer it is possible to get relatively cheap accomodation at Ringerike folkehøgskole.