Children integration in a new school in Hungary

Look, look, look. Search, research. Find what schools will be in your vicinity. Visit the head, have good chat, find out what the head is like, his aim, motto, personality, as that gives direction to the school. Ask to go and see what a day is like, ask to sit in the class your child is likely to join. Get a feel for the place, if it is possible visit an open day together with your child.

If you have money to pay for something different, there are alternative schools and alternative for schools still providing the same certification.

To get into a normal state school the headmaster will decide if to take your child on based on the information you give and by interviewing the child and/or an entry test for level of knowledge to place the child in the right form. By law the local state elementary school cannot turn away children from their catchment area, although I am not sure if that is the case for foreign citizens too.

There are also denominational schools run by churches that are free, some tie admittance to participation and church attendance.

Otherwise you can pay to send your child to private schools that might be using a different curriculum to the national one, other methods or set up or a different language, albeit there are free minority (eg German, Croatian speaking) and bilingual schools too.

Other options available are learning groups (parents pay a teacher or a group of teachers to teach their children in a place they rent/purchase), some calling themselves schools or academies or homeschool groups, of which they are neither, but most often than not these group secure examination opportunities with a state approved school, where the children get their official half-yearly and end of year reports, certificates. These are small, child-centred alternatives with usually a good athmosphere and good marks achieved.

Yet another option is home education, which is similar to the learning groups, but you have to arrange and register with a school for exams and you have to either arrange tuition or teach your child to pass the exams.

Whichever route you decide to go down, children are flexible. They pick up the language fairly quickly, although it does help if they already know some words, expressions and some teachers, private tuition to help them along. If they are capable readers and writers, you can use the Duolingo app for learning Hungarian; it is quite good from probably age 8-9 onwards.

It might help to enroll them to do some sports with other kids, where language does not play as big a role.

If you can, leave time for the child/ren to get accustomed to the new surroundings, new culture, new everything before heading off to school. Try to find other expats in your area or some other ways to help them find friends or mates to play/hang out with, to connect with.

Sometime, kids do get upset about the upheaval, talk it through.

The Hungarian state schooling system involves a lot of sitting and learning and homework and tests and stress, lots of books to carry around, rules and regulations for teachers and kids. Monday to Friday school starts early, schooldays are long, after school there is a lot of homework and homestudy, memorization and recitation, extracurricular activities. You get good and bad points or marks and grades for petty things and written tests the same. But a good teacher can make your child forget about any difficulty they face and give them wings and a smile.

Hope this answers your questions to some extent.
All the best with your move!