People with access to NSA recordings are listening to (recordings) of Trump's calls and his staff's calls. The Presidents phone is currently tapped by American intelligence agencies.
They then leak the details to the press.
The spy could be holdover Obama appointees now full fledged government employees, NSA/FBI/CIA/name that spy agency who don't like Trump, neverTrumpers or the Russians.
It is perceived that the leakers are trying to damage the Trump Presidency. The leaks generally are to press agencies who are liberal.
Flynn may or may not have had a conversation with the Russian Minister that items of great substance were discussed. Since the conversation occurred in December before Trump took office many say it could have not been much. But he did resign, so, there is more to the story. Most likely Flynn will not be the last victim of anti-Trump spies, just the first successful one.
The story you are not hearing much of is that some are using American intelligence resources to spy on the President of the United States and his staff. This is very bad.
Look for more leaks as Trump and Pompieo try to root out the leaks. This will be very messy. Good sites to follow are: Rantburg.com, Drudge, Breitbart, WAPO, WSJ. You'll get both sides of the story if you hit them all. I listed the more Conservative sites first.