I often saw my grandma drying basil leaves in direct sunlight by spreading them on a clean cloth for several days. Is this a good method? I feel like placing the herbs in the open air like this will contaminate them with dust. Is there any other method I can use to dry fresh herbs?
Many of us lack sufficiently reliable sunlight and use a food dehydrator. These may be electric, but can also be solar, accelerating the process compared to open sun-drying. They have to be ventilated, to allow the moisture to get out, but still significantly reduce exposure to dust (and also stop the herbs blowing away).
Solar dehydrators can easily be made from readily available materials, even scrap, and there are plenty of plans online. All you really need is a clear plastic container with holes in the sides (holes low and high on all sides will improve airflow) and to spread the herbs in a thin layer. If drying thicker things they may need to be raised on a grid to allow the bottom to dry out.