What are "natural" ways to make my knee swelling go down?

Many: "natural" remedies (i assume you are referring to non-medication, non-surgical means) for knee swelling include rest, ice, elevation, an elastic knee brace, physical therapy and massage.

Try ice: Bromelian capsules (or found in pineapple) is a known antiinflammatory.

Ice: Icing and elevating are commonly recommended to decrease swelling. Usually 20-30 minutes on (make sure there is something between your skin and the ice pack) can be repeated a few times a day until the swelling resolves.

Rest compression ice: Decreasing activity (especially the ones that cause swelling, rest, ice, compression (ace wrap) and nsaids are all reasonable ways to help treat knee swelling. To figure out why your knee is swelling, an examination, x-rays, and perhaps an MRI are often needed.

Reduce swelling: Ice for 24 hrs when selling occurs then moist heat and rest.