The easiest, most effective method I've found is to find a big chain building supply company that's convenient for both you, the designer, and your distant painter. Then look through paint chips until you find the colors you want and send the names and numbers to your painter, who visits his own store and buys (or matches) the paint. Voila! Color matching on remote control.
You could also use Sherwin Williams' new ChipIt! and save yourself the trip to the store. (Earlier POST.)
In this case the show is The Whipping Man in Fort Worth, but I choose the base colors here in Dallas at my local Lowe's, from the Olympic brand paint chips.
Olympic paint colors from Lowe's
The creams and tans will be the "white" of classical columns and the darker "stone" floor. The mahogany color will be for the faux mahogany (eventually plus wood graining and TLC). The green subs for wallpaper, and the purples for a distant view of destroyed Richmond, Virginia. (Post with set elevation HERE.)
Odds are my painter will buy some colors of paint and mix others from the theater's stock. Unless for a special effect, paints are normally flat latex.