A panini press is versatile, relatively cheap, and easy to use for quick meals, but you need to clean it regularly to prevent build-up from grime and oils.
Wipe the panini maker down or clean it after every use while the plates are still warm. After making your panini, unplug the machine and allow it to cool slightly.
Take a damp towel or paper towel and gently wipe the surface of the plates to remove any grease or stuck-on ingredients. The warm plates should be easy to clean.
If the press is grimy, scrub the plates with a towel soaked in hot, soapy water. For hard-to-clean spots, use a mix of baking powder and water and wipe it off after 10 minutes.
You can also clean between the ridges using the thick end of a chopstick wrapped in a damp towel, allowing you to use more elbow grease when cleaning the hard-to-reach indents.