I think a good way about it is to read as much as you can but focus on the experiences of the people who lived through it and not so much on the history of it. Sure, it's important to know the reasons behind the Troubles and why there was so much tension, but how did it affect those who lived at the time? Was there a curfew? Where were the no-go zones if you were Catholic or Protestant? Were there stop-and-frisk tactics employed by the British Army and the Northern Ireland Police? How did mixed families deal with the situations? I think that would make your characters more rounded than a straightforward history of the Troubles. How has it influenced your protagonist? Are there things he does, certain ticks or something, because of what he witnessed in the Troubles? (Like, does his heart race when he sees a British soldier in uniform or the police on patrol?)

As for how much is too much....enough is when you really feel like you know enough about them to accurately represent them. If you can find people who lived through the Troubles or went there at the time, their stories could be very useful. Good luck!