Well, I can`t tell much about the main differences between private and public schools, as I have never visited a public school.
I started school at the age of 6 what was one year earlier then most others somehow (I`ve always been one of the youngest). Primary school (Grundschule) takes 4 years and afterwards you may choose another kind of school you wanna visit. Usually your parents and/or teachers choose it for you. It depends on how your grades were and how you fit into school in general. There are three common kinds of school you may visit after primary school that are called Hauptschule, Realschule and Gymnasium. Basically you can say if you go after grades Hauptschule is the lowest, while Gymnasium is the highest form of school. There are other forms of school too like the Gesamtschule and stuff like that, but I can`t tell much about it. I guess Gesamtschule is a kind of mixed form of school.
Anyway, I entered Gymnasium after primary school (my parents wanted me to enter Realschule, but my teacher wanted me to enter Gymnasium). Gymnasium took 9 years (it has changed now to 8 years in Germany). After these 9 years (grade 13) I made my Abitur which allowed me to enter University (and here I am).
If you go to Realschule or Hauptschule after Primary School, you don`t stay 9 or 8 years. Usually Realschule takes 6 years if I`m not mistaken. Hauptschule should take that long too (both til Grade 10).
When you leave Haupt- or Realschule, you usually enter apprenticeship. You aren`t allowed to study at university.
Anyway, there are plenty of other alternatives. If you finished Hauptschule, you may continue going to school and try to make a Realschulabschluss (a certificate as if you finished Realschule). You may also try to make your Abitur even if you haven`t visited Gymnasium.
It`s a little complicated to explain.

Well, now to my school life.
At Grundschule (Primary School) we usually were in one classroom and there was not much need to change. We visited church once in a month, but that`s not everywhere the same. We had subjects like Maths, German (of course), Sports, Religios Education, later English and something that was called Sachkunde (like Biology, Geaography etc. in one subject).
The teachers came to our classroom (usually...of course not for stuff like Sports).
(and I hope everything I tell you is true, cause it has been a long time since then and I was young )
Later at Gymnasium we had to change classrooms more often. In 5th and 6th grade we were still in one classroom most of the time, but from higher grades on (especially from the 10th grade on) we needed to switch rooms regularly (after every lesson or second lesson). We had subjects like Maths, German, English, Biology, Geography, Chemistry, Physics, Religious Education, Arts, Music, History etc. Later we could choose between Latin or French (I took Latin) and from 11th grade on we had to choose between more subjects (like if we want to do two languages or two sciences etc....a little too complicated to explain).

Hell I`m writing since more than one hour now. I guess that`s enough for today (cause it`s around half past 2 am now ) I hope I helped you a little. Continue asking if you need to know more. I will answer all questions if I can (but not know, cause I need to go to bed )