Who is entitled to child care benefits (børnepenge)?
If both parents live in Denmark the payment is automatically sent to the mothers NemKonto. Read more about NemKonto at What is a NemKonto (Easy Account)?
The allowance is paid the first coming quarter after registration.
The current child care benefit rate can be found on the taxministrys homepage. Note that the homepage is in danish. The age of the child is shown in the left column and then first the yearly amount and next the monthly amount in the right columns.
For more information regarding who can recieve child care benefits see Which public subsidies can I get with a newborn?
Find the prices for child care here (site is in Danish).