According to Wikipedia, the other 3 reactors at the Chernobyl power plant continued operating and producing electricity for many years after the accident, with the last reactor closing only in 2000 (!). Who worked there? Where did they live? How did they get to work every day?

The other reactors at the power station were practically undamaged by the initial explosion and after the sarcophagus was constructed it was relatively easy to thoroughly decontaminate the actual power plant complex which was a contained, closed-off space, unlike the majority of the exclusion zone.

It's worth noting that the exclusion zone, including the towns of Pripyat and Chernobyl, was also decontaminated, but to a lesser degree due to the nature of the territory and its size. Soviet scientists had relatively effective ways to decontaminate radioactive areas - for example the so-called barda, or draff, the suspension of ethanol, which was used as an effective plasticizer to remove irradiated particles, but some of the more effective and targeted measures were only practical on a relatively small scale, which was why the "deep" decontamination of the power plant itself was seen as doable, but was not extended to the surrounding areas. What is not generally known is that while the most important phase of the clean-up was conducted in 1986-1987, the clean-up itself lasted well into the 90s, so the power plant was not the only local operation still active after 1986.

So as I said, with the remaining reactors undamaged, the power plant's territory effectively decontaminated down to safe levels, and after the sarcophagus was finished and the 4th reactor was completely isolated from the rest of the complex, the power plant was ready to resume work.

As it was, the Chernobyl plant was still an enormous investment and one that was still perfectly capable of producing electricity, with the nominal power capacity of 3000 megawatts after losing reactor 4 (for context, Leningrad Nuclear Power Plant, currently the largest operational Russian nuclear power plant by power output, has a nominal capacity of around 4200 megawatts, while Bruce Nuclear Generating Station, the world's largest nuclear station by output, has the nominal capacity of around 6200 megawatts). One would have to construct at least 6 or 7 conventional coal or diesel plants with the average output of around 400-500 megawatts to make up for the lost output, so it was still economically viable, especially considering that the actual operating risks were now considerably lower, seeing as the surrounding area was already evacuated.

In order to house the remaining workers an entirely new town of Slavutych was set up around 50kms away from Chernobyl and 70 kms away from Pripyat, with the first residents moving there in late 1987. A large portion of the initial residents were evacuees from Pripyat who also formed the bulk of the remaining power plant work force, which amounted to around 9000 people at its peak (almost half of the town's entire population). While initially the workers had to commute by bus to the power station, in 1987 the authorities also finished the construction of the new Semykhody railway station within the exclusion zone, which allowed for direct rail travel between Slavutych and the Chernobyl power plant and became the default commuting route for the plant's remaining workers. The radiation levels were low enough for the workers to continue both traveling to and operating the plant, so long as they remained within the heavily decontaminated areas of the station and relied on the newly constructed infrastructure.