The NY Times and the Washington Post don't prosecute. They inform, and Congress and various Federal agencies investigate. Actually, state bodies can investigate as well, that's how Spiro Agnew got prosecuted.
Trump is in office less than 100 days, and already even Republicans are joining in the investigations.
Now here's an interesting situation. Tomorrow the Senate oversight committee is going to ask who did the wiretap that then-national security advisor Michael Flynn was caught talking to the Russian ambassador. If a wiretap is set up for national security without a warrant, only foreigners can be wiretapped, American citizens cannot be. If a foreign national calls up an American, you are supposed to turn the recording off, or something like that. Tomorrow, one of three things will happen.
1. The Senate oversight committee will be denied an answer, which has never happened before. OR
2. The investigating agency admits it broke the law. OR
3. The investigating agency proves wiretapping Flynn along with the Russian ambassador was legal because a warrant was issued to wiretap Flynn during a legal investigation. Which means that Trump appointed a national security advisor who not only had a show on RT, Russia's propaganda network, and who was working for the Turks, (he just registered retroactively as a foreign agant). Flynn was also the target of an ongoing investigation. Which if true, is sure to add momentum to even more investigations about where the hell Trump finds these appointees.
Hang in there Finn. The fun is just beginning.