Kids here start kindy at 5 (actually, they youngest they can be is 4 years, 11 1/2 months old). Elementary school goes up to 6th grade, middle school is 7th and 8th, and high school is grades 9 - 12. We have no public preschools, but most parents here send their kids for 2 years before kindergarten.
It's a little different where I live. They must be 5 on or before Sept 1 of the current year to start K (Kindergarten) and school starts 4 days prior to that, so they could be 4 days shy of their 5th birthday. However, you don't have to start at 5, you could wait until 6 (redshirting), which is very common here starting with May birthdays. School starts the last couple days of August and goes through the first week of June, then summer break. The next August they would advance a grade (provided they learn all the material).
It goes K, 1st, 2nd, 3rd, and 4th for elementary.
5th and 6th is intermediate school.
7th and 8th is middle school.
9th (freshman) has its own campus, but is considered part of high school.
10th (sophomore), 11th (junior), and 12th (senior) are high school.
Then it's off to college where advancement is based on the number of hours you complete successfully rather than years. Some colleges have semesters, others trimesters.
Preschools are not public in general here (I know several states do have public preschools), but high risk students (including lower income) can get public pre-k. Our preschools generally have a toddlers class (18 months as of Sept 1 of the current school year), 2s (2yo as of Sept 1), 3s (3yo as of Sept 1), and 4yo are pre-k, where they learn the skills they must know to start K. Each class is age appropriate--i.e., toddlers just learn about taking turns and sharing. Most parents start at 2yo, some wait until 3 or 4, but not a lot. K teachers around here can really tell which kids went earlier and which went later (or not at all); most would tell you to send them by 2 or 3.
ETA: K is full day. It is not mandatory. The only thing our state says is that you either have to be homeschooling or start 1st grade at age 7 on September 1 of the current school year. You could turn 8 September 2. Also you can start 1st grade as long as you are 6 on September 1 of the current school year, but you could also start K at age 6 on September 1 of the current school year.
If you want to get a child in younger (say one that turns 5 September 2), you can go to private school that allows it (mainly Montessori around here) and once they successfully complete grade 1 they could transfer to public school (starting with 2nd grade)