How did the red dwarf get brought back to life?

Answer 1

It's all to do with 'nanobots', tiny machines that were a part of Kryten's self-repair system. These were said to have gone missing during the events of the last episode of season V, 'Back to Reality', after which the crew lost their mothership Red Dwarf, spending Season VI in Starbug.

Even though they continued following Red Dwarf's signal, it turned out that the ship was a lot closer than they imagined. The Nanobots had disassembled the ship, creating a nano-sized version for themselves inside Lister's laundry hamper, while turning the excess matter into a planet for safekeeping.

At the end of season VII, Kryten convinced the nanobots to rebuild the original ship, which they did, though they made it way too big, considering it was vast enough to start with. Also, they resurrected the original crew, who have no knowledge of the original disaster that killed them, or any events in between then and their revival.

Answer 2

Red dwarfs do not die and come back to life. They are stars that have low mass and burn hydrogen slowly over billions of years. They eventually transform into white dwarfs after they have exhausted their nuclear fuel.