We don't know for sure because the books are filtered through Katniss's first person POV and she doesn't know about the conspiracy until later. We do know that Beetee is a tech genius who is shown to be capable of hacking into Capitol television programs to broadcast rebel propaganda. It isn't unreasonable to assume that such a person would also be capable of making a few surveillance cameras turn in the other direction.
Also, we know that Katniss and Peeta go on the roof of the Training Center to talk privately which suggests that there are a few places in the Capitol where one can have a private conversation. The older victors would probably be more familiar with such locations than Katniss and Peeta.
Finally, Plutarch Heavensbee shows Katniss his watch which when viewed from the correct angle shows the mockingjay. At the time, Katniss thinks this is just one of the Capitol's trends, but later it seems like Plutarch was trying to communicate to her that he was with the rebellion. This suggests that rebels within the Capitol during this period communicated using a good deal of subterfuge -- by hidden symbols and coded language, for example.