To the best of our knowledge, they did not. We know very little about intelligence gathering in Trajan's rule, but quite a lot about intelligence gathering in the Year of Four Emperors because Tacitus wrote a very detailed history of it so my examples are going to have to be from that.

Much of what they found out was from diplomatic missions from Germanic tribes petitioning Rome to help them with something. For example, under the reign of Galba (68-69 AD) several tribes along the Rhine river became embroiled in a land dispute and appealed to Galba to sort it out. These envoys were normally asked general questions about goings on beyond Rome's borders and members of the Praetorian Guard reported on their conversations. The tribe that lost out, the Ligones, then sent envoys to the legions on the Rhine to complain about it to them. They chatted with officers and soldiers until the local governor ordered them to leave, all in the hope that these legions (which were openly contemplating rebellion at the time) might "correct" Galba's judgement. Tribes were more than happy to broadcast everything if they thought it might help them. If the envoys were not sent to the emperor directly, then a governor would write a letter informing the emperor of the developments.

Another way Rome was aware of what the Germanic tribes were up to were traders. Trade between the germanic tribes and Rome was abundant, so traders were a great source of information. It was not unusual for members of the Praetorian Guard to hang around in bars chatting to traders about their trips in an attempt to gather intelligence. There is no source outright stating this, but from context it seems highly likely. For example, when Otho had Galba murdered in a coup, he searched Galba's office only to find reports of multiple mutinies and rebellions along the Rhine river and in Britannia, which Galba could only have discovered through traders because the very people who would normally tell him these things were the ones rebelling. There was also another incident where the governor of Hispania wrote to Otho to tell him that Hispania accepted his rule, but he then recieved reports that the governor was lying and that the legion there had mutinied. Again, the only way he could have heard this was from the traders that supplied the army since the governor was outright lying to him.

However, sometimes these methods were insufficient and a proper factfinding mission was required. We are fortunate to have Germania by Tacitus. Tacitus was a prominant senator and historian who was asked to conduct an ethnographic survey of the Germanic tribes, you can find it here: http://www.gutenberg.org/files/2995/2995-h/2995-h.htm Trajan would have used this in conjunction with what was learned from traders and envoys to construct foreign policy.