Get a bike to move around in CPH!
With a Rejsekort, each trip costs about 40% less. You just have to top it up every now and then at metro stations. When you enter a metro station or a bus, you will have to check your Rejsekort in at one or the big, eluminated blue dots. Once you leave, you will have to check out and the ticket price will be deducted from your account.
An anonymous Rejsekort can be issued to anyone and you can let anyone use it. You will have to top it up at a station. Keep in mind that you need to have a minimum of 70dkk on your anonymous Rejsekort in order to start a journey.
Once you’ve got a Nem-ID (link to Nem-ID article), you can get yourself a personal Rejsekort. They can be linked with your bank account so that they are automatically topped up once your balance gets too low. Minimum balance for a personal Rejsekort is 25dkk. To one like these, you can also add a commuter area to your account. This is especially useful for DTU students. In addition, you can take longer distance trips across Denmark with a personal Rejsekort but not with the anonymous one (although of course you can also buy specific tickets for these trips).
NB. I would strongly recommend the anonymous Rejsekort before you are able to get a personal one. You will have to go to DTU a few times during orientation days, and paying the cost for single tickets can quickly add up.
Copenhagen is not a terribly big city so most of the time it is also fine to walk everywhere.