Where do orphanage kids go to school?

Not too many orphanages around these days.

There are often purpose built children's homes run by local authorities. Some by charities and some by certain religious organizations.
When it comes to education, as far as possible, integration within normal school settings is preferred.

Many youngsters have certain behavioural and educational needs which are defined through the statementing process.
Schools are selected which can best meet their educational need.
So many attend local comprehensive or junior schools. Although you can imagine the difficulty many have when the subject of 'family life' crops up at school.
Those with educational or emotional difficulties often have care plans in place at school to help them and the teaching body meet the child's needs as far as possible.

For those that require a specialist education environment advice is often sought through social workers; educational psychologists and others to determine the best possible learning environment.
Application is then made to specified school, if it's thought the child is a good candidate they are invited to look around, if there's a sense that it might be a good fit trial periods are arranged and if successful that wil be the base for their education.

There are No orphanages!!
Just foster homes and detention centers for the incorrigible.

I had a friend that was an orphan and she went to public school. Sometimes though they are schooled at the facility where they live.

They are in local school districts, and attend the public school in that district.

Pessent school or public school