Home Dialysis. Here's a great website that will give you more information than what i can provide in a brief answer: http://homedialysis.Org/. In my opinion, the information provided is accurate and very useful for the lay public.
2 kinds. One is for hemodialysis, a simpler form of the machine available in dialysis units where the patient &/or family member is trained to connect via IV line or graft to clean blood. Another is for peritoneal dialysis which connects via abdominal tube to instill liquid in abdomen and take it back, along with waste, in a periodic fashion during sleep. Training and monitoring are easier for this one.