While more and more cities improve bike related facilities such as the lanes and rental system, Denmark (especially Copenhagen) is always leading the world, and it keeps improving and expanding!
A pedestrian needs to be aware of no only vehicles but also a very high traffic flow of bikes when crossing the road, and a biker is no difference to a vehicle driver.
I strongly recommend you to rent a bike to explore Copenhagen and experience its bike culture. It is still worth doing that even the daily rental price is not really cheap. Check this out: Donkey Republic.