I may or may not prepare a "should I tell the truth" flowchart to help you navigate life in a non-Ned Stark manner, but in the meantime here is Vularai's Maxim:
If asked a direct question, answer it truthfully, but do not otherwise volunteer the truth freely, and do not contradict the inferences made by others to try and fill in the gaps that arise from living thusly unless asked to do so directly.
Example: I was sharing a meal out with my girlfriend--who knows little about my unsavory past--when she said something along the lines of, "That's because we're both only children." Now this is untrue, she simply inferred it because I have never spoken of my sibling (whom I have not spoken to in 15 months now, and have no intention of ever speaking with again), but instead of going, "Actually..." and ruining the meal with an infodump about my benighted kindred, I simply let the conversation move along and didn't engage with that.