Today, 12:47 AM
The first big step is awareness. Check out wireshark, it is a tool that you can set up to read all the data going back and forth between your network device and other devices. You can have it running in real time, it will autoscroll like a log, where each line is a packet. If you don't know what they all mean, it's OK. The point is to explore and learn.
One thing you will notice off the bat is whenever you are doing stuff like reading websites, the output will start showing a lot of HTTP packets, which stand out because wireshark can color code packets by protocol, etc. You can also see other machines on the network when they broadcast, and the things your machine broadcasts. The most common broadcasts you should see are using address resolution protocol (ARP), this is when a device sees the MAC address of another device and doesn't know which machine to ask to get its IP address. Even from ARP packets, you can learn some details about the other machines. Assuming everyone is using their real MAC address, you can often identify the type of device (printer, switch, gaming console, desktop NIC, wifi adapter, etc.).
Anything going over HTTP, you can see in plain text. But some apps will encrypt and then use HTTP to communicate, so all you see is the encrypted text. HTTPS is encrypted. In the old days, I have seen IM conversations via wireshark, IM clients today *should* be encrypting that stuff. A VPN tunnel encrypts and goes over a lower layer like TCP, so all the ISP sees is encrypted traffic between you and the VPN. You can use a tool like wireshark to verify stuff like this.