A window has broken in the storm.

Get everyone out of the room, close the door, and keep shoes on anyone who has to go back in. Then cover the opening from the inside rather than the outside, because working on a ladder in wind is how a broken window becomes a hospital visit.

The cleanup waits until the covering is up and the room is photographed.

Covering it, in the order that works

Clear the loose glass from the sill into a rigid container, not a trash bag. Bags tear and then the glass is on the floor and in someone’s hand.
Measure the opening roughly, including the frame.
Cover from the inside while the weather is bad. Rigid material is best: plywood, a sheet of hardboard, even a cut down cardboard box for a small pane in a pinch, taped or screwed to the frame, then plastic sheeting taped over the whole thing to shed water.
Tape the perimeter properly. Wind gets under a loose edge and takes the whole cover off, usually at three in the morning.
Only go outside to board once the weather has passed, and only if you can do it safely from the ground.

Plastic sheeting alone flogs itself to pieces in wind and does not keep the weather out for long. It is a stopgap over something rigid, not a substitute.

Then deal with the room

Move soft furnishings and anything absorbent out.
Roll back rugs, which hold both water and glass.
Vacuum, then vacuum again the next day. Small fragments travel much further than anyone expects, and they surface for a week.
Check the room below and any adjoining room for water.
If the rain came in for a while, treat it as a water event: the drying window is 24 to 48 hours.

Keep the evidence

Before you clear anything:

Photograph the window from inside and outside.
Photograph whatever broke it, if it is identifiable. A branch, a piece of a neighbor’s fence, hail.
Photograph the room, wide and then close on any damage.
Keep the object that came through, if you can do it safely. It is the difference between “a window broke” and “a branch came through the window in the storm”.
Note the date and time.

The wider documentation habit for any storm claim.

Insurance

A window broken by wind, hail, or flying debris in a storm is normally covered, and so is the water damage that came in through it while it was open. What usually is not: a window that failed because the frame had rotted, and glass that broke from thermal stress or from settlement.

Two practical points:

The deductible may make it moot. A single broken pane often costs less than the deductible, particularly where wind and hail carry a percentage deductible. Report it anyway, then decide.
Emergency covering is usually reimbursable as reasonable mitigation, so keep the receipts for the board, the sheeting, and any board up service.

If the window was broken by something that came from a neighboring property, that is still normally your own claim first. Whether their insurer ends up paying depends on negligence, not on whose fence it was.

Getting it replaced

Get the opening measured properly by a glazier rather than guessing, especially for a double glazed unit, where the spacer, the gas fill and any coating all have to match what is there. A mismatched replacement pane in a run of windows is visible from the street.

If several windows went, ask about matching. Some policies address matching explicitly, most do not, and it is worth raising before the work is agreed rather than after.

The short version

Room cleared, door shut, shoes on. Cover from the inside with something rigid and tape the whole perimeter. Photograph before you clear, and keep whatever came through. Report it even if the deductible may exceed the repair, and keep the receipts for the emergency covering.