(The information below is accurate as of 19th September 2017)
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.
Train and metro tickets can be purchased at the DSB ticket office in Terminal 3 at Copenhagen Airport. You can also buy various types of tickets at the designated ticket machines in Terminal 3 and at every train station around Copenhagen.
You can buy a Rejsekort at the airport, which is an electronic ticketing system for travelling by bus, train, and metro. Rejsekort unites the different transport operators, travel zones, ticketing systems and discount schemes into a common system, which makes it easier for passengers to use public transport services in Denmark. With Rejsekort you need to check in and check out at the train station when getting on and off the train and metro. When traveling by bus you need to check in and out inside the bus. The card costs 80 DKK (the card price is non-refundable). You must expect to add 170 DKK to the balance to cover the cost of travel. Find it here.
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.
Please note that you cannot buy tickets on the train. Without a valid ticket you risk being given a fine on the train.
Here you can see a map showing Øksnehallen (DGI Byen), the conference location, and its immediate surroundings: