The cleanliness of the work surface and its construction will help you protect the fabric from damage. The work surface should be constructed of a sheet of unsized muslin. The muslin should be stretched over a polyester or cotton batting to pad the surface. Over the muslin another loose sheet of unsized muslin should be placed. The loose sheet of muslin should be washed or changed regularly to keep it clean.
Muslin is used because it absorbs dust and dirt and thus prevents it from dirtying the fabric.
If you don't have any muslin you can work on a clean towel. Working on a hard surface, even if it is clean, will make the fabric dirty. The dust settles on the hard surface and then your needlework becomes the dusting cloth.