I don't use Apple products but my kids want to. How can I manage Family Sharing?

It can be done using one device, but it is a bit more difficult using only one device. On the device, sign into iCloud with your Apple ID and set up Family Sharing. Create the child's ID. Sign out of your ID and sign in with the child's ID. Swap iCloud sign in as required.

From the article below.

One adult in the family—the family organizer—can set up Family Sharing for the group from their iPhone, iPad, iPod touch, or Mac.

Family Sharing - Set up.     

Family Sharing.