ISO: Bread starter

I can remember helping my grandmother bake bread. She used what I think was a starter. She only used yeast to start it and then used it over and over until she decided she needed a new batch. Each baking day she would remove some and add back ingredients so the yeast would grow. I know it included boiled mashed potatoes, flour, milk, and sugar. She said she didn't understand why people spent money buying yeast all the time. I would like to grow this or a similar yeast starter. Could someone help? Would appreciate it.