The process involves several steps: 1. Application of a crystal violet dye. 2. Addition of iodine, which binds to the dye and traps it in the cell. 3. Decolorization with alcohol or acetone. 4. Counterstaining with safranin. Gram-positive bacteria retain the crystal violet dye and appear purple, while Gram-negative bacteria do not retain the dye and appear red or pink after counterstaining.