Copenhagen has an extensive network of public transportation, covered by metro, S-train, city busses as well as regional busses and trains. You can get anywhere in the city within short time.
When you arrive at Copenhagen airport, you can take the train to Copenhagen Central Station. You can also take the metro to various stops in the city - the metro does not stop at Copenhagen Central Station though. The metro runs every 2-4 minutes during rush hour, every 3-6 minutes outside of rush hour and every 20 minutes at night. If you take the metro to Nørreport Station, one of the inner city stops where almost all S-train lines arrive at, and from where you can go anywhere in Copenhagen. The S-train will take you to almost everywhere in Copenhagen, with six different lines going back and forth between various stops. The S-train lines at Nørreport all stop at Copenhagen Central Station as well (depending on which direction they are going) and will take five minutes to get there. The S-trains run every 10 minutes during rush hour and every 20 minutes outside of rush hour and on the weekends.
The S-train is supplemented by regional trains that you can catch from Copenhagen Central Station. These trains will have stops in different parts in the outskirts of Copenhagen and in other regions. If you want to go somewhere the does not have a train stop close by, you will likely be able to find a bus that can take you there instead.
To best arrange your travel plans, you can use Rejseplanen, which will show you exacly where you need to walk, which trains and busses to catch and at what time.
You can buy a 72 hours ticket to public transport in Copenhagen delivered on your phone for 200 DKK. Find it here.
If you want to explore the city, you can buy a 72 hours ticket which give you free admission to 73 museums and attractions, free public transport and discount on restaurants, attractions and entertainment for 629 DKK. Find it here.
Here you can see a map showing Øksnehallen (DGI Byen), the conference location, and its immediate surroundings: