Cleaning your drawing tablet should be a regular part of how you care for it. I recommend cleaning your drawing tablet once a month - and more frequently if needed.
Depending on the brand of tablet and the kind of tablet you'll find that manufacturers provide different advice for cleaning. For example, some manufacturers say it's OK to clean the tablet with isopropyl alcohol. While other manufacturers explicitly indicate that you should not use isopropyl alcohol.
Below are a few links I found from different brands about how to clean their tablets. It may not be comprehensive but it's a start.
STEP 1 - First, I remove dust from tablets, pens, and monitors with a microfiber duster. Specifically this one: the OXO Good Grips Microfiber Hand Duster ($12) that I bought on Amazon. The red microfiber brush can be detached and easily cleaned in a laundry machine and then dried on low heat.
STEP 2 - I gently wipe down the tablet with a damp cloth or towel
OPTION 1: If the tablet is a little greasy I may put a bit of soapy water on the damp cloth. I want to emphasize that the cloth is damp and not wet. You shouldn't have any water drops coming off the cloth.
OPTION 2: Since September 2024, for pen displays I've switched from soapy water to using a screen cleaning sprays (WOOSH and MISTIFY). more here: Screen cleaning sprays.