Whether you're using blood cells or fibroblasts (which is what's taken from foreskin, and can come from a simple skin punch too) you give the cells a big blast of growth factors trust turn on genes that are expressed very very early in gestation, back when a fertilized zygote is starting to turn into all the different cell types in the body. These are induced Pluripotent Stem Cells (iPSCs). Then you can freeze these, and use them to make neurons, cardiac cells, pancreatic cells, whatever.

There are techniques for reprogramming that bypass this by going from blood or fibroblasts to neurons or something. This is called direct reprogramming. It's more complicated and less mature technology, though, so it's not practical for most cases.