In the scenario I'm envisioning, my group is in a city. They've got a source of hydroelectric power, but a few downed power lines/utility poles are making it difficult for them to transmit the electricity. We're far enough post-apocalypse that they don't have any petroleum and can't use a car with a crane attached to it. Would it be feasible for them to design a crane or simple pulley system that could get the pole upright again (using the materials that might be readily available to them in a city, of course)? Is there another way they might get the job done?
One of the issues with doing this is that righting the pole is not enough. They're likely working with 11kV or even 33kV lines (depending on the country, but it'll be in this ballpark), which are under high tension. They would need not only to put the pole back up, but the re-tension the lines. Without the proper equipment, this going to be difficult. Furthermore, when the poles fell down, some of the lines probably snapped, which means they'd have to repair or replace those lines too.
My suggestion is, that they'd want to have access to the correct equipment, and a working knowledge of how high-tension transmission lines work before attempting this.
That's not to even begin on the issue of replacing and broken insulators, fuses, or switchgear...
Even to this day, people are lifting objects even heavier than an electrical utility pole to upright them in this manner. Think of the stereotypical Amish barn-raising scene where an entire wall of a building might be raised into place and held there while worked on. Yes, you could use a pulley system, but you probably don't need to.
You start with your utility pole on the ground. If there is not already a hole in the ground for its bottom to rest in, then dig one.
An "=" represents the tree A "+" represents the hole A "," represents the ground (the comma is grass) ========== ,,,,,,,,,,,,+,,, +
Make 3 or more ropes, tie them all to the top end of the pole you want to raise. Then make a smaller pole that will help you lift the top end of the utility pole up by pushing on it. With the bottom end of it inserted into the hole in the ground (or at least partially in it) to stabilize the location of the bottom, push up on the top to get it as high as you can.
A "-" is the smaller pole that you are pushing the bigger one up with A "." is rope ==... == ... - == ... - == ... - == ... <--(people, animals, or devices pulling on end of rope here) ,,,,,,,,,,,=,,,,,,, +
Then have people with ropes on the other side of it start to pull to raise it the rest of the way.
With ropes in place, minimum 3 at 120 degree angles from each other, you should be able to stabilize the pole so that it does not fall over since it is held back from each direction.
Once it is upright and in place, just make sure that it has good footing in the hole in the ground you have put it in. If you are unsure, leave the ropes in place and anchor them to act as guy lines to support the pole.
Here is a video of practically the same thing being done, though not for electric utility: (Thanks to @Bald Bear for the comment suggesting this video)
@Aaron above has correct answer on raising the electric poles without a crane. But there are a few other solutions to the broader problem of restoring electric service.
There are large cranes that work off electricity, for use in arctic conditions. They do trail a cable behind them, but it only needs to be long enough to reach the next pole. Even if they do not have such a crane handy, they can modify an gas-powered crane (using the same tools and skills that they used to fix the generator).
Electricity can be carried without poles, by a heavily insulated cable, that is typically buried in the ground, but could be left just laying on the ground in the short term (you just do not want any human or animal to break it accidentally). There are few cables big enough to power a large city, but there are plenty that can power a small village. Poles are used more IRL b/c they are easier/cheaper, but that is only true if you have a crane.
If it's a small community, it makes sense for them to live at or near the hydroelectic dam. River & reservoir are good for fishing, transportation, irrigation. Moving the community might be easier than fixing a long power line.