Timeslides were an accidental invention created when Kryten used mutated chemicals to develop photographs.
When Kryten decided to use the photo processing lab on Red Dwarf to develop some pictures, he was amazed to see the photographs come to life before his eyes. Holly surmised that the developing fluid Kryten had used had mutated over the last three million years. When Kryten converted some of the photos to slides, the projected slides also came to life.
When Lister walked toward the first slide, which was of Frank Rimmer's wedding to Janine, he found that he could enter the photograph and interact with the wedding party. Frank found Lister's intrusion annoying and began to hit him. Lister tried to walk away, but found that he could not leave the frame of the picture. He had to escape by the way he had entered, through the lens of the camera.
Other slides created included a random couple's skiing holiday and one of Hitler's Nuremburg speeches. When Lister stole Hitler's briefcase, he inadvertantly prevented an assassination attempt on the Nazi leader. The Boys from the Dwarf discovered that they could use the Timeslides to alter history.
Lister used a picture of his teenage self to make himself a millionaire. He gave his younger self the idea for the "Tension sheet", a simple but lucrative invention developed originally by Rimmer's schoolmate Fred "Thickie" Holden. Lister then vanished to live a new life as a rich industrialist. Kryten and the Cat also disappeared, since Lister was responsible for their being on Red Dwarf. (and in the case of the Cat, the existence of his entire race)
Rimmer decided to beat Lister at his own game. He used a picture of his boarding school dormitory to create a timeslide and went back to give himself the Tension sheet. Unfortunately, Holden overheard him talking to his younger self and reached the patent office first. The timeline went back to much the same way it was before, except that somehow Rimmer was no longer a hologram. This did not last very long as Rimmer blew himself up. (RD: Timeslides)
The timeslides were never used again, perhaps for fear of perverting the timeline. When the Dwarfers found themselves in 21st century London, science fiction shop owner Noddy suggested that they could use the timeslides to get about. The Dwarfers explained that, like all his other suggestions, the timeslides were back on Red Dwarf. (Back to Earth, Part Two)