Life on this planet requires carbon to function. Carbon is consumed by eating or by absorbing CO2 from the atmosphere and using it to create sugar via photosynthesis. If you completely black out the sun, then photosynthesis stops. In the long run, all the carbon on the planet will end up either in the atmosphere or dissolved in the ocean. I'm not sure if we would run out of O2 or food first, but if I learned that the sun would never come up again, I would probably take my life in my own hands.
We can use energy to power lamps to grow plants, and replenish our oxigen and food supply that way. Actually i think this would not be so difficult. Humans humans require very little oxigen. Almost all oxigen in the world is consumed by smaller animals, many which are not essential to human survival. Also with increased CO2 levels farming will be easier, and if we stop eating meat we will need far less farms than we have now.
At the start we should burn as much fuel as possible and store the energy in hydrogen cells before all the smaller animals have consumed the O2. We can then use this energy to build a new energy infrastructure. This could be based on a combination of nuclear, geothermal and hydroelectric, or perhaps wind if that still exists.
I think humans would adapt and survive. At first we would have to make large sacrifices and investements, but in time life will be very comfortable again.
Wildlife as we know it however will die out and basically the world would become a desert with no air to breathe and no food to eat. Zoo's will contain remnants of what once was. Think men living on mars.