The air filter is the part of your vent hood that removes particulates and smoke from the air before pushing it outside of your house or recirculating it. There are two kinds of filters: a metal filter and a charcoal filter. Both of these kinds of filters can be easily removed for cleaning or replacement.
For a metal filter, use degreasing solution and cover it completely -- then clean it fully with warm soapy water. Charcoal filters will need to be replaced, but this can be done yearly.
To prevent a difficult to control fire, de-greasing your hood and vent is important. Spray or apply your degreasing solution (white vinegar/water works great) to all non-electrical components and remove with a soapy sponge. Nail polish remover can be used as well as it breaks down organic substances. Use a microfiber cloth for a clean finish.