Short answer
Contain the water inside, relieve pressure on a bulging ceiling safely, photograph everything, then get a roofer to tarp or temporarily seal the leak. Don't climb onto a wet roof; permanent repairs wait for dry weather.

Inside the house first
Put buckets and towels under drips and move furniture and electronics away. If water is near a light fixture, turn off that circuit at the panel.
- If a ceiling is bulging with water, keep people out of the room.
- Poke a small hole at the lowest point of the bulge over a bucket to release water, standing to the side.
- Check the attic with a flashlight to find the wettest spot and put a container under it.
Document before repairs
Photograph ceiling stains, wet insulation and any visible roof damage from the ground. Note the date and weather. Your insurer will want this.
Get the roof covered
A roofer can tarp or temporarily seal the leak even in bad weather, then return for permanent repairs once the roof is dry. See emergency roof tarping and roof leak repair.
Questions
Should I go on the roof to find the leak?
No. Wet roofs are slippery and dangerous. Check the attic from inside and let a roofer handle the roof.
Is a leaking roof an emergency?
Active leaks during a storm are, because water damage to drywall, insulation and electrical grows quickly.
This guide is general information, not professional, legal or insurance advice. Follow your insurer's instructions and local codes, and put safety first.