Since gold doesn't tarnish it's a lot easier to clean than sterling silver. This is for most gemstones (rubies, diamonds, sapphires) but super soft ones like pearls, opals and coral should be cleaned separately. Here's what you'll need: 

1. Soft bristle toothbrush

2. Bowl

3. Warm water

4. Mild dish soap

Soak jewelry in the warm water that has a few drops of dish soap in it for 20 minutes. Then gently brush the jewelry with the new soft bristled toothbrush. Getting all the grime and oils and dirt that lodge around stones and in crevices. Rinse with cool water. Use a microfiber towel to dry. Be careful not to use a paper towel, as the fibers in it can mark up soft gold pieces. 

Another option for gold cleaning with harder stones (no soft or porous stones), and if you are feeling a little lazy, is to use warm or hot water, a couple drops of Dawn or Palmolive and swish your jewelry in the warm water and then leave it overnight. In the morning take it out and rinse it clean, it should come out nice and sparkly!