Flying to Copenhagen

The easiest and most convenient way to travel to Denmark would be to fly to Copenhagen (Kastrup, CPH). The airport is situated 8km south of Copenhagen and has very good transportation options to Copenhagen city center and the rest of Denmark.

If you are under 26 years old, take note that SAS offers all year round discount "youth tickets" (it might not be the cheapest so check other companies, but it could be an option and doesn't show up on flight search engines).

You could also try to fly to Malmö in Sweden instead because they work with some of the cheaper airline companies such as Rayanair or Wizzair.
There are different buses to Copenhagen centre from there which travel to copenhagen:
Once you are in Copenhagen, it is very easy to go to the venue with public transport.

Other ways of getting to Denmark

Driving to Roskilde is simple, but don't forget to take into account that it is located on an island and you will either have to drive over a toll bridge (prices are here if you are coming from Germany prices are here if you come from Sweden) or take a ferry, which can add some costs to your trip.

You could also consider taking the train or the bus to Roskilde or Copenhagen but make sure you check the flight prices because in some cases it might not be cheaper and would take a lot more time.

Public transport system

Travelling within Denmark is quite easy once you understand the public transport system. First of all, Denmark is divided into different regions and in this instance we are going to describe the prices and the way things work for the Zealand region since this is where the competition will take place.
Zealand is divided into zones and they will determine the price for your trip. In the vast majority of stations and bus stops, you will be able to find a map such as this one:



This particular map describes the different zones if you start within central Copenhagen which is highlighted in red. Of course the map will be different depending on where your starting point is.

The different colours show you how many zones you will need to pay for:
So all you need to do is find your destination on the map (good luck if you have no idea where it is :D) and see how many zones you need to pay for.

If your destination happens to be right in the middle of two zones, it is the lower amount of zones that counts. So in this case travelling to Hellerup (between blue and yellow, at the very right of the map) would cost 2 zones, not 3.

Another easy way to check how many zones your trip will be is to use Rejseplanen. This is pretty good option because you will also be able to plan your trip and find out how to get to your destination, how long it will take, how to get there, etc. and the website is available in English!
Just look for your wished trip and then click on "see more" then "see the price for this journey". You will be able to see the number of zones the trip will cost near the "total fare with Rejsekort" title.
Note that the price with Rejsekort indicated on the website might not be what you will have to pay (since the Rejsekort is a special card used when you travel a lot in Zealand, but you will most likely not have one).
You can find the actual price of your trip under the "other product" tab. Prices are shown for single tickets (billet) and for 1 trip on a 10 trip ticket (klippekort).

Ok, so now the only thing left is to actually buy your ticket. You will have two options there: either buy a one way ticket or buy a klippekort which is a 10 trip ticket and costs a little bit less per way. You can buy the single tickets anywhere (at counters, at the vending machines, in the buses) while you can only buy the klippekorts at counters and vending machines.
To make your ticket valid you need to stamp it before you start travelling. You can do that by inserting it in the yellow machines situated on the platforms or inside the buses. Those machines should then clip part of your ticket and stamp it with a date. You're now good to go!

About the kippekort: they are very nice and convenient to use because they allow for a lot of flexibility. If two persons are travelling 8 zones, you could stamp an 8 zones klippekort twice, or a 4 zones klippekort 4 times, or a 5 zones klippekort twice + a 3 zones klippekort twice. Basically it doesn't matter which cards you clip or how many times you clip, as long as the total amount of zones you need to have is there.
You can find the prices for all klippekorts here. Note that "voksen" means adult and "barn" is child (under 16 years old).