Firstly, you should get some goggle cleaning solution or generic eye glasses cleaner spray from a sporting goods shop or online, and the cleaning solution should be plastic-compatible which is not bad for the plastic lenses.
Secondly, drop some cleaning solution on one half of the soft lens cloth. By the way, you should make sure the cloth should be soft and 100 percent cotton. Wipe the lenses with the half of cloth with cleaning solution until the dust and grime has been got rid. Do this step twice.
Thirdly, dry the lenses with the dry half of the lens cloth to polish the surface. And you wipe them carefully and gently. Besides the above mentioned way, I think you can have your goggle cleaned in a professional shop, maybe the one you bought it.