How does one determine intracellular concentration?
In fact the line that you quote doesn't mean that the solution is formulated to be identical to the cytosol. All that it means is that the solution should be buffered to physiological pH (typically slightly alkaline); should contain a relatively high concentration of sodium ions and a low concentration of potassium ions; and should be isotonic (i.e have the same osmolarity as the cytosol) to avoid osmotic effects such as plasmolysis (shrinkage due to loss of water) or osmotic lysis (bursting due to uptake of water).

There are many such solutions, but a commonly used simple one is phosphate buffered saline. Another is Ringer's solution. If the aim is to keep the cells metabolically active these are often supplemented with glucose or lactate, depending upon the cell type.

Addendum in response to comment from OP

According to the WP entry for Ringer's solution, Sydney Ringer determined the requirement for Na, K and Ca salts in a specific proportion when carrying out experiments with perfused frog hearts. This was in the late 19th century. A  Google search measurement of intracellular ion concentrations reveals current methods.

This review starts off with a discussion of early measurements of intracellular pH (see page 298). Basically these all consisted of making cell lysates, with various attempts to prevent post-lytic changes. If you do a Google search determination of intracellular pH you will find lots of current methods.