How do I sample color from on-screen and apply it as texture in a model?

[DanRathbun]

You may be speaking of the Sample Paint feature, (this only works within SketchUp.)
This feature is the eyedropper button on the Materials inspector panel.

SketchUp User Guide

• Creating a 3D Model
  • Adding Colors and Textures with Materials
    • Applying Materials
      … which says:

Tip: To sample a material that’s already in your model, hold down the Alt key to change from the Paint Bucket tool to a Sample tool. With the sample tool’s eyedropper cursor, click the face whose material you want to sample. Release the Alt key to return to the Paint Bucket tool.