I am not sure if I understood your question correctly and also this is not my main field of knowledge, even though let me try to make my contribution with this (not final) answer.
Stem cells can be categorized into several groups depending on their ability to differentiate:
Totipotent: can differentiate into all cell types;
Pluripotent: can differentiate into almost all cell types;
Multipotent: can differentiate into a related family of cell types;
Oligopotent: can differentiate into a few different cells;
Unipotent: can produce one cell type only.
Once you have a culture of stem cells those are stimulated to differentiate
As long as the pluripotent stem cells are grown in culture under appropriate conditions, they can remain undifferentiated. To generate cultures of specific types of differentiated cells, scientists may change the chemical composition of the culture medium, alter the surface of the culture dish, or modify the cells by forcing the expression of specific genes. Through years of experimentation, scientists have established some basic protocols, or “recipes,” for the differentiation of pluripotent stem cells into some specific cell types article
Stem cell differentiation is tightly regulated by signaling pathways and modifications in gene expression.
The major chemical or physical signals include: Growth Factors; Cell Culture Substrate; Co-culture Environments; Signal Inhibition; and epigenetic processes such as DNA methylation and chromatin remodeling.
"How does one get started in doing this"
To be useful for transplant purposes, stem cells must be reproducibly made to:
Proliferate extensively and generate sufficient quantities of cells for replacing lost or damaged tissues; Differentiate into the desired cell type(s); Survive in the recipient after transplant; Integrate into the surrounding tissue after transplant; Avoid rejection by the recipient’s immune system; Function appropriately for the duration of the recipient’s life. article
on the same article there is a note that could be a partial answer to your second question: "why is this not at all common to find as a service"
Currently, the only stem cell-based products that are approved for use by the U.S. Food and Drug Administration (FDA) for use in the United States consist of blood-forming stem cells (hematopoietic progenitor cells) derived from cord blood. These products are approved for limited use in patients with disorders that affect the body system that is involved in the production of blood (called the “hematopoietic” system).
and there is another FDA disclaimer about this subject website
