Basically everyone gets evacuated from the affected area and are staying with friends and family in Reykjavík. Grindavík is a very small town compared to the rest of the world. The government has offered to buy properties from the ones who cannot return, since the erruptions have been going for a few years in that area and there's no sign of stopping.

To answer your question for the rescuers, researchers, and workers left in the area, once the eruption starts it's quite easy to predict the flow. Luckily there are a few other roads without the risk of lava flow, mainly due to lava diverting barricades. In case of emergencies they use helicopters.

Other parts in eruption risk zones would be similar, since it's just not worth it for people to stay in those areas and most people can stay with family. And repairs to the road are usually pretty quick when the eruption dies down.