This is an overview over the way publically funded childcare is organised in Copenhagen, Denmark. I will be noding the different "stages" soon.
In Denmark the law concerning social service (the Service law - Serviceloven) guarantees every parent the right to be able to get their child cared for during weekdays, roughly between 6.30 am and 5.30 pm, thus leaving the parent free to go to work. The guarantee affects children from 6 months to, at the time of this writing, 12 years. It used to be up to 14 years, but recently - at least in the City of Copenhagen - drastic cutbacks and general downsizing has meant that they have cut short the guaranteed period of day care by two years, to save money.
Ideally the parents should be guaranteed a place in a vuggestue when the child reaches the age of 6 months, although most professionals recommend that the parents wait until the child is at least 12 months old. The fact of the matter is, though, that due to bad planning and downright incompetence many kommuner are desperately short on daycare options - but that may be for another node.
The child can remain in the vuggestue until it is 2 years and 10 months. Not too long ago the rules said "3 years", but as the effects of said poor planning became obvious they needed to free up spots for the smallest children by transferring the older lot to børnehave (lit. children-garden)1 as quickly as possible. So the age criteria were changed to make up for the blunders.
From vuggestue the child moves on to børnehave, where they'll stay until they're ready to start 0th grade, or kindergarten class. As soon as the transition to school is made, the child will go on to next level: Fritidshjem, lit. "Free time home".2 Here the child can stay until it turns 10 - or begins in 4th grade, whichever comes first. After that it can start in the Fritidsklub ("free time club").
The child is guaranteed a spot in the club until its 12th year. After this, due to recent cutbacks, it's a question of how many members the club has room for. Too bad, since kids around the age of 13 really shouldn't be roaming the streets with nothing better to do than to cause mischief.
Any of the first two institutions can be replaced with dagpleje, ie. a person employed by the city/government to take care of two or three children in the person's own home. The only real difference is the fact that the child will not be subjected to a large group of other children, and will only have one adult to relate to. This can be both good and less good: the physically smaller dagpleje is on the one hand less intimidating, but the possibility of forming bonds is greatly diminished. Dagplejere (the people employed in dagplejen, who are, btw. not necessarily trained pedagogues) have different places where they can meet, and let the children play, thus introducing them to other children.
Parents pay for this service, but not the full price. 2/3 of the total cost is covered by the government, and the rest is covered by the parents. If a parent is unable to pay, due to low income, or no income at all (though that is technically not possible in Denmark) the parent/s can apply for "subsidised child care". This will almost always be granted, based on the reasoning that children will be a lot better off having some good and solid grown up role models in a day care, instead of, in extreme cases, roaming the previously mentioned streets, or falling victim to neglect, mental as well as physical. Also based on the fact that if a parent do not have some form of daycare for smaller children they are not considered "available for employment", and can therefore not get unemployment benefits or "welfare".
A positive side effect of the latter has been3 that many immigrant families who, traditionally, have no concept of institutionalised childcare, have been forced to send their children off to børnehave in order to be able to collect welfare. As a result the children have had a much better grasp of Danish when they started school than those kids who never went to børnehave.
Although resident Danes often find the system flawed and sometimes annoyingly bureaucratic, it is, all in all, a fairly good system. And no system can be better than the people managing and administering it.
- Yes, Children-garden is Kindergarten, but in Denmark this has nothing to do with school. Kindergarten class, or 0th class is closest to what most other countries call Kindergarten (Kindergarden).
- The City of Copenhagen (Københavns Kommune) is the only kommune left with Fritidshjem. In the rest of the country the kids are being cared for in a "School/free time facility" (Skole/fritids ordning or SFO), located within the school premises.
- The very right-wing party, Dansk Folkeparti, wanted to make it compulsory for immigrant children to attend pre-school daycare, but no other parties would back that up based on the "racist" nature of the proposal.
Sources: My own experience after 14 years in the business.