For what a set-up looks like, you would have soil(chemical-free) and if you want, a drainage layer at the bottom. Since, red-backs are territorial you would need multiple hides, which can be achieved by placing lots of wood pieces around the tank.
As for plants, ferns would be good aesthetically. Moss can be used, and it adds to the humidity.
Mist the soil so it is evenly moist but don't over mist until it gets soggy. Keep the humidity at 50-60%.
For food you can feed small earthworms, fruit flies, isopods, or slugs. In the wild redbacks eat many different arthropods.
One last thing, remember you don't want to build a rainforest for these salamanders, because they occur in temperate forests. Too much humidity could cause mold and fungal problems in your tank, and would be unnatural to your salamanders.
Good luck on building the temperate vivarium!