Basically, I use an UV light air purifier in my system, which helps reduce the mold, mildew, and other airborne allergens from forming.. I use this exact product: https://amzn.to/2XqaN8Q
In addition, I clean mine annually with a vacuum and compressed air to remove dust. The product above really makes my annual cleaning much easier and the air in my home is cleaner.
For the homeowner all you can do is replace the filter once a month. I use pleated air filters. If your not familiar with furnace internals best be left to the pros. You would't want to damage anything or get hurt. If you or someone has allergies a UV air purifier would help a little.
You should really have it serviced once a year, that includes cleaning.
I agree with Kelli. Have it serviced professionally once a year. It's not too expensive, and it's worth it to have someone knowledgeable clean your furnace.