I usually embroider on linen or cotton without any backing but embroidery experts who use very fine fabrics or are doing stumpwork or other, heavier projects use a muslin or maybe lawn backing. When working with small pieces, basting the fabric to be embroidered to a larger piece that can then be mounted on a frame or in a hoop is advisable. Great Britain and Australia have a wonderful heritage of skillful, artistic embroiderers and great publications.
Embroidery should be worked so that there isn't loose, floating or carried-over thread, yarn or floss so that the back of the project is as tidy as the front. Knots on the back are no more acceptable than knots on the surface of a quilt.