Every commune/gemeinde seems to work a little differently, in my experience, but you cannot go wrong giving advance notice and let them decide how they want to handle it.
There is an application form in all cases, and you will need to provide a photo.
The birthdate will be used to determine which class they will be placed in, but there can be exceptions to this.
As you will discover, children do need what might appear to be some unusual things to bring with them to school. Ask for a list rather than leaving this to the last minute. These items may include the following:
PE Kit (shorts, t-shirt and non marking running shoes)
indoor shoes for the classroom (these are left at school and the shoes they were outside and left outside the classroom door
bathing suit and towel (some schools offer swimming classes)
knapsack
school supplies (coloured pencils, etc)
Outdoor clothing so they can walk to school in all weather, initially they may need a rainjacket, rainboots and an umbrella. On nicer days, a sun hat.
Try not to worry, kids will sense this and this makes them more anxious. Look at it as an adventure. Start reading up on healthy snacks to take to school and involve the kids in your research. Teachers are quick to note which moms send healthy snacks.