We did dialysis on our elderly kitty. You introduce normal saline IV solution under the cat’s skin with an IV needle and instill about 250 ml. You need to do this a couple of times a week. I’m a former paramedic and my wife is a nurse, but the process was hard on us and very uncomfortable for our cat. At best you are buying only a few days. In the end we made the tough decision to have him put to sleep after his kidney failure advanced to causing seizures. There comes a time when you have to let go. However, consider adopting a new kitty. All of out three cats are from animal shelters.
I actually have 3. Kitty is my eldest. They are all "throw aways". The last one Mimi was a stray that decided to stay in our backyard (probably because I gave them crunchies).
I took her, well him, in last January because I could no longer bear the guilt of having her outside. I took her to the vet to have all tests and shots (I did get all my cats their immunizations shots once, when I first got them).
But Kitty was my first responsibility since I left home and has been with me for almost 19 years now (12/9 is our anniversary).