Prefix your message with /s to chat to your squadron, or use /s on its own to switch to squad chat.
Get a list of chat commands in-game
by typing /help into the chat box
For the win!On PC you can set your Squadron channel to be a separate tab in the comms panel. This can be done by going to the last tab of the comms panel and changing "Squadron" from "Main" to "Tabbed". Then when you switch back to the first tab of the comms panel you will see Squadron as a separate channel and you can communicate there without using /s.