There are many buses in Copenhagen. A-buses (for example 1A, 2A, 3A etc.) run frequently and have many stops in the city. S-buses (for example 350S) run less frequently and have fewer stops, so you get through the city faster.
You can see the timetables for the buses on the Danish website, but it is easier to plan your journey using Journeyplanner.
There are also three harbour buses that sail across and along the harbour. They have the same ticket system as the rest of the public transport system in Copenhagen.