Probably is a guide, but experience, for me, dictates the following:
Since you're primarily looking for low DC voltages (with some sort of meter) but might encounter Mains AC:
Making absolutely sure that all parts of your body are not grounded -
1: Always connect your ground lead first (using an insulated probe) and only to the circuit ground, NEVER the chassis ground
2. while holding the positive (red) probe ONLY, very carefully touch it to the point (connector, pin, wire, etc.) of interest.
3. Do not allow the probe to slip from the point of interest
4. Only when you're confident the probe will not slip, quickly take the reading. Then remove the probe.