There are many ways to clean a dirty or greasy range hood. You can use different kinds of solutions to eliminate any grime.
You can dust it and use hot water and dish soap to remove dirt. For the more stubborn grime, try a vinegar solution for degreasing.
It's also best to NOT use brushes with sharp bristles to prevent any scratching or damage to the range hood.
Besides the materials available at home, you can also consider store-bought cleaners and degreasers. It's best to use environmentally-friendly products to help maintain your range hood.