For conductors that the helicopter cannot safely hover close enough to for the line worker to work on from the helicopter, they sling load the worker below the helicopter, lower him down to the conductor he needs to work on, and he attaches himself to the conductor and detaches from the helicopter, and the helicopter moves away from the lines.
When the work is done, the above is reversed to extract the worker.
There's a segment showing this in "Modern Marvels" episode S11E45, "Wiring America" starting at 23:44 [1].
I've also seen a documentary somewhere [2] that was similar but more focused specifically on line work. That had a clip showing a worker being lowered to a particularly difficult to reach conductor. There were at least 3 horizontal layers of conductors, with at least 3 parallel conductors in each layers, and the one needing work was in the middle horizontally and had at last 2 layers above it.
For that one, they had several dry wooden poles connected end to end to form a kind of chain. They put this together in a dry area, then had a crew carry the pole chain outside careful to not let it touch the ground, so it would not get wet from the morning dew on the ground. One end was attached to the helicopter, which slowly started lifting it, with the crew that was holding it making sure to not release segments until they were sure they would not swing into the ground on the way up. Finally, the line worker was attached to the last segment. From then on, it was similar to the segment from Modern Marvels.
They used the dry wooden pole chain because there was no way to reach the work conductor without whatever was suspending the worker simultaneously touch two of the above conductors, so it was imperative that this not short out things.
I believe they used a pole chain rather than some non-conducting rope because a rope can get tangled in things or wrap around things. The pole chain consists of rigid segments, which are not going to get wrapped around anything.
[1] https://youtu.be/vuRNs50VMJ0?t=23m44s
[2] Probably on the History Channel or Discovery Channel.