Nursery starts at 3 or 4 (depends when birthday falls) then they start primary one when they're 4 or 5. Then right through to p7 age 10 or 11.
In p7, you complete the form that decides secondary admissions. There are protestant high schools, catholic high schools, and mixed schools. Enrollment criteria varies for each, an older sibling at school, proximity to school etc. Grammar schools are more academic and to attend these children must take the exam set by the school, and get a high enough grade to get in. We used to have the 11+, one test the pupils took whose grades determined where they went, but the council abolished that, and now if a child lists 3 potential grammar schools they want to apply to, they have to take 3 tests. Or they can choose to not take the test and not apply to a grammar.
The grammar schools are usually private, and cost a good deal more in fees, it varies from school to school. The GCSE exam board (who set the exams) is CCEA, but some schools use mainland exam boards, AQA, etc. It goes from first year to upper sixth (5th year, 6th year, upper 6th). Fourth year is the first year of GCSE's, fifth year is the second. At 16, children can choose to leave school. Or, if they get the relevent grades, they can stay an extra two years, and do A levels. (They can also do A levels at Belfast Met, a sort of technical college).
The "Education Authority" has replaced the BELB in Belfast has the department that oversees education.
www.eani.org.uk/i-want-to/apply-for-a-school-place-or-transfer-between-schools/primary/
League tables are a good place to start with secondary schools, published in the local papers and usually available online. Co-ed is common at primary level, but less so at secondary age.