When the extension starts up, it does some feature detection (for websockets, webrtc) and a connectivity test (to the bridge). If everything is passing, it should display the string, "Your Snowflake is ready to help users circumvent censorship" (or, the equivalent translation). That's currently the indication that it's working.

Note that, by design, there are many more snowflakes than users, so it may take a while before accepting a connection.

We're working on better ways to communicate that the extension is being useful in,
https://trac.torproject.org/projects/tor/ticket/31109