If you know your computer's IP address, you'll know the addresses of your
network. There are many ways to check your computer's address.
From the network icon in your desktop panel, select "Connection Information".
There you'll see "IP Address:" and your IP address next to it.
What I do is use a terminal, by typing:
ip addr
There you'll see a numbered list of devices and information about them. Each
device has a label such as lo, eth0, eth1 or wlan0. Devices like eth are
used when you are connect via a LAN cable. Devices like wlan are for WiFi
connection. The lo is a special virtual device, used for connecting to
yourself.
If you're using a wireless connection, then read the information of wlan0.
There you should see inet and your IP address.
If your IP address is 192.168.1.107, then your network is 192.168.1.0/24. The
/24 means your local network is the addresses from 192.168.1.0 to
192.168.1.255. If it was /16, that would mean from 192.168.0.0 to
192.168.255.255.
As I understand, if you set Postfix's mynetworks option this way, computer's
on your you'll local network will be able to send emails from your server.