I don't know your area but when I enrolled my girls into their public school (they now go to a private school), it was very easy - even with my limited Portuguese. You need to take your and kids identification, vaccination report for your children and proof of residency.
The first cycle is for grades "pre, 1, 2, 3 and 4"
The second cycle is for "5 and 6" grades (my 10-year-old daughter will be starting 5th grade in September)
The third cycle is for "7, 8, 9, 10, 11 and 12" grades (my 12-year-old daughter will be starting 7th grade in September)
What I would suggest if visiting the school that suits the grades of your kids and enrol them. Most schools would be closed now but the offices reopening in September. The school year is due to start in mid-September.
They will have a list of school books for you to purchase for the year. We would go to the local newsagency and put our names down for the "bundle of books". We would then return to collect them.
From my experience, I did everything at the school directly, not at the council office.
Let me know if I can help more.