The answer is a sequence rather than a principle, and the sequence is the answer. Every step in it exists to stop germs moving from one place to another.
Before you start. Clean your hands before touching the dressing: jewelry off, hands wet under warm running water, soap, 15 to 30 seconds including under the nails, rinsed and dried with a clean towel, or an alcohol-based cleanser. Then make sure you have all the supplies you need handy, and have a clean work surface. Gathering supplies after washing your hands undoes the washing.
Gloves, in two specific situations. Use clean medical gloves if the wound is infected (red or oozing) or if you are changing the dressing for someone else. They do not need to be sterile.
Between stages. This is the most important part and the part people most often rush. The old dressing goes into a plastic bag; the gloves come off into the same bag; hands are washed again. New gloves for cleaning the wound. Hands washed again. New gloves for the new dressing.
Handling the new dressing. Do not touch the inside of the dressing. For a packed wound, keep the moist gauze off the skin and only in the wound.
Afterward. Put the used supplies in a waterproof plastic bag, close it tightly, double it, and put it in the trash. Wash your hands again. Wash any soiled laundry from the dressing change separately from other laundry, and ask your provider if you need to add bleach to the wash water. And use a dressing only once. Never reuse it.
What not to use is part of the same question, because the urge to reach for something stronger usually comes along with this one. Do not use skin cleansers, alcohol, peroxide, iodine, or soap with antibacterial chemicals. These can damage the wound tissue and slow healing. A damaged wound bed is not a cleaner one.