Lay a soft cloth on a flat, stable surface. Cotton baby diapers or terry cloth works very well.
Mix a solution of mild dish-washing soap and water in a spray bottle, using a small amount of soap. The water dilutes the dish-washing soap and makes it safer for the 78s. This is a cleaning solution that works on 78s from the 1940s and 1960s. Purchase a professional cleaning solution for 78s that were manufactured prior to the 1940s.
Lightly clean the record label with furniture polish. Spray the polish on a soft cloth and wipe the label to remove dirt and grime. Don't saturate the label. It should stay fairly dry. The furniture polish also makes the label more water resistant.
Put on gloves to prevent getting oil and fingerprints on the 78. Lay the 78 record on the cloth. Gently polish and clean the record surface with a terry cloth working with the grooves. Using only the cloth, it is possible to remove most of the dust, dirt, and grime.
Spray dirtier areas with the cleaning solution. Clean the grooves with a fine-bristle brush to remove dirt and grime from the bottom of the grooves to the surface of the record.
Rinse the 78 with a damp cloth and clean water several time to remove soap residue. Use distilled water for the final rinse.
Dry the record with a clean, dry terry cloth. Set the 78 in an upright position in a dish rack to air dry.
Turn the 78 over and repeat the procedure on the opposite side.