It is very easy to get into Copenhagen from our house. Avedøre Station is a 5-minute walk from the house, and on weekdays there is a train every 10 minutes into Copenhagen.
The train is Line A (the blue line) towards Hillerød, and it runs 7, 17, 27, 37, 47 and 57 every hour. The train journey to Copenhagen Central Station takes 10-12 minutes.
Several different buses also run by the station.
Tickets
We recommend that you as a tourist buy a City Pass. With it you can get around the entire capital by S-train, metro and bus. Children under 12 come for free with an adult: https://www.publictransport.dk/tickets/city-pass
Otherwise use the DOT-app: https://dinoffentligetransport.dk/find-billetter/dot-billetter-app which is cheaper than buying tickets at the station.