How do electricians know where the line is down?
Customer service power lines are typically segmented into blocks or rings, so that damage to part of the grid does not disable a huge geographic region. A substation may feed several separate customer grids near it from a large regional power line.

Each customer grid has its own circuit breakers at the substation, which are usually outfitted with automatic reclosers. During a power failure, you may notice the power go off, come back on, go off, come back on, and then go off a third time and stay off. This is due to automatic reclosing, which attempts to immediately restore power. Some line failures such as a falling dead tree branch are brief, and power can be restored immediately after the tree branch has fallen past the line.

If the fault can not be cleared, the faulting line segment is usually immediately reported by the recloser or substation to a regional electric grid control center. It is often completely unnecessary to call in a widespread power failure during a storm, as the control center knows immediately when a line segment has lost power.

For example, automatic reclosing on Youtube:

Smart Grid - Self Healing - NOJA Power https://www.youtube.com/watch?v=rVTIwr1Rk2c

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There is no way to instantly pinpoint the location of a fault on a line segment that cannot be automatically restored. These faults are typically located by linemen getting into a utility truck and driving around the neighborhood inspecting every part of the line segment. They have detailed maps to guide them. Multiple utility trucks may be assigned to inspect the down segment. If you see a electric utility truck slowly driving down the street during an outage, it is because they are visually inspecting the lines.

When there is an outage at night, utility trucks are equipped with high power lighting. The utility trucks will drive slowly along roads with one person aiming the spotlight, and another person looking at the illuminated lines and equipment to check for damage.

This is part of the reason why an outage that can't be automatically reclosed may take several hours to be restored, due to the linemen needing to drive around and inspect all the lines to check for broken wires, damaged insulators, heavy ice weighing down lines, or objects contacting the lines.

And this is also why the customer's local power lines are segmented into small areas, because the larger the customer line segment, the more time it takes to drive around during an outage to locate the fault. The driving to look for line problems takes even more time in adverse weather conditions such as a blizzard or freezing rain.

For example, on Youtube:

How Power Gets Restored - Puget Sound Energy https://www.youtube.com/watch?v=gLikTRjrmnc

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Once the power line fault is discovered, the linemen will take additional safety measures to ground and/or short-circuit the power lines, so that in the event power is restored before their work is completed, the safety grounds will immediately re-trip the line breakers and prevent injury to the linemen.

Safety grounding also protects linemen from home power systems which could be miswired to backfeed power into the inactive line. A small home generator is capable of backfeeding into a down power line and energizing it at its 12,000 volt (or higher) operating voltage. Safety grounding and shorting of the down power line assures these miswired home generation systems will result in blown fuses or burned out home generators, rather than a dead lineman.

For example, on Youtube:

Protective Grounding https://www.youtube.com/watch?v=T0vZDl2kFI8

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For the very large transmission lines that feed a region (the poles are much taller than local grids), these are often cross-country and may not be near roads. Access to these lines for inspection and repair can be done by ground vehicles, but access is difficult in the winter or when there has been rain and the ground is soft and muddy.

Inspection and repair work for these very large transmission lines is instead often done by helicopter, and due to the helicopter not being in contact with the ground, they can approach a live power line, make contact with it, and work on the line to do maintenance or repairs while it still is fully powered.

For example, on Youtube:

Helicopter Maintenance on energized 765,000 Volt Line https://www.youtube.com/watch?v=x94BH9TUiHM

'Hot-Washing' the Insulators of a 500,000 Volt Power Line! https://www.youtube.com/watch?v=lcjhjna9jZE