Obtain a moisture meter from a local hardware or home improvement store. There are pin and nonpin versions. The pin versions will only work with materials soft enough for the pins to penetrate (wood, carpet, drywall, etc).
Turn the unit on and wait thirty seconds to two minutes for it to calibrate. Instructions for calibration will be included with the unit.
Press the sensor pins (or detection surface if you're using a nonpin unit) into the roof joists in various locations and take moisture readings. If the moisture level reads above five percent, there's a chance for the joist to bow and cause structural damage to the roof.
Identify the source of any intrusive moisture by tracking upward from the point where moisture was first detected.
Obtain a thermal imaging camera from a local rental company.
Turn on the thermal imaging camera and calibrate it by taking the temperature of a nearby wall with a surface thermometer and adjusting the thermal imager to match the reading.
Point the thermal imager at the roof joists. Areas that are lower in temperature (usually blue or green on the thermal imager screen) are likely to either be poorly insulated or suffering from water leakage. The thermal imager is far faster than a moisture meter and the source of leaks can be easily identified by the color patterns on the thermal imaging screen.