For more minor and occasional condensation you might just see the signs that it had occured at some point but had dried out - the boards might be dry but over time will become water stained and darkened. This is also sometimes seen on the top of insulation. Over 15-20 years or so the top of the insulation turns quite dark and takes on a crusty surface. For more serious occurences you will find the boards damp and for very serious stuff it will be soaking wet and will smell musty - or worse.
The technical test is with a decent quality damp meter. A moisture content above about 16% indicates some dampness above normal atmospheric. MC above 20-21%...ish will cause timber to decay and could bring on dry rot if the temperature range is right.
