I'm looking for a good workflow to use the same colors in, for example, a new file in InDesign or Illustrator.
is there a "best practice" workflow to use the same colors in different programs?
Create swatches (in whatever App you start in) then export swatches as an .ase file.
In every other app you can load the .ase file into swatches.
.ase files can be loaded into any Adobe app which uses swatches.
Web sites such as Adobe's Kuler.com will also allow you to save themes in an .ase format.