IPv6 is here and confuses me

Your ISP will delegate a prefix for you, probably /48 for your business, unless you have a contract that specifies a different size. For example, 2001:db8:cafe::/48. You will then break that prefix into separate /64 networks. For a /48 prefix, that means you can have 65,536 different /64 networks: from 2001:db8:cafe::/64 to2001:db8:cafe:ffff::/64.

It is pretty easy to see which networks belong to you. If any of the first 48 bits delegated to you are different, e.g. 2001:db8:beef::/48, then you would see that addressing does not belong to you.

With just a couple of exceptions, You will use /64 networks for your IPv6. You could further subnet one or more of your /64 network to /127 for point-to-point links (prevents ping pong attacks) or /128 for things like router loopbacks.