Possibly using spies and black bag jobs. Update: Further Snowden documents confirmed NSA used spies in Germany & Korea. The undoubtedly excellent engineers at Deutsche Telekom couldn't find how the NSA was tapping them. "Reporters for Der Spiegel, working in collaboration with The Intercept, contacted Deutsche Telekom and NetCologne several weeks ago in order to give them an opportunity to look into the alleged security breaches themselves. The security departments of both firms say they launched intensive investigations, but failed to find any suspicious equipment or data streams leaving the network." Those NSA guys have to be really good to fool the Germans.
We all "knew" that surveillance was everywhere, but continuing revelations from Laura Poitras & Edward Snowden remain startling. The latest report suggests heavy use of undercover agents and physical intrusion. That's what spies do, after all. England's GCHQ is deeply involved, along with the Aussies and the Canadians.
There's every reason to connect the French and German spies with the American. Snowden reported the U.S. had access to millions of phone records every day from France. The NSA denied they were tapping the French. A few days later it came out that it was French intelligence doing the tapping then sharing with the Americans.
I'd bet that the U.S. has more effective surveillance than the Russians. Russia is an authoritarian nation where government faces almost no restrictions. Russian computer scientists are world class but I doubt they have the money or the expertise to match the Americans.
Remarkable reporting at
https://firstlook.org/theintercept/2014/09/14/nsa-stellar/
and a major NSA document I would assume counterfeit if I didn't know the source.