Transferring money to and from Denmark is not particularly different to transferring money in any other country. There are a range of transfer agencies available for transferring money abroad.
Most, if not all money transfer agencies charge a fee for the transaction. Therefore, for smaller payments, it is probably worth using a foreign card at an ATM. You will probably have to pay a fee for withdrawing from a foreign account, but this fee is almost certain to be less than what you would have had to pay to an agency.
For larger payments, there are international agencies for transferring money such as Western Union or MoneyGram. Transferring money to and from Denmark via these agencies is very simple: The sender goes to an agency in their country, pays in the money and states which foreign agency the money is going to. The receiver then goes to the respective agency, identifies himself with ID and can pick up the money immediately.
However this convenience comes at a hefty price, so you might want to check out other options. In many cases it is cheaper to transfer money via an online service such as PayPal or Moneybookers, though you need an account with the service in order to do so.
Fees on international bank transfers very much depend on how much money you want to transfer and between which countries. For bank transfers within the European Union, you use the EU Standard Transfer. The EU Standard Transfer is relatively low priced, although the transfer must be in Euros and must not exceed € 12,500.00.