You can drive to Vesterbrogade, where you can normally park on the side streets. Be aware that in many cases the parking in the area is not free of charge. Use Rejseplanen to find the way to and from Vesterbro. There are also bike paths along Vesterbrogade.
Directions to Vesterbro

Take the bus or train to Vesterbro. There are several bus stops around Vesterbrogade and you can also use the train to visit the area. The closest station is Copenhagen Central Station (Københavns Hovedbanegård) and it takes only few minutes to walk from the station to Vesterbrogade.