Use ordinary soft, clean dust cloths, chemically treated dust cloths, vacuum cleaner brush attachments, or other available ordinary household aids. The paint surface of the slats is quite smooth and dust is easily brushed off if done at regular intervals.
To vacuum, use the brush dust head attachment and tilt the slats first up, then down (but not entirely exposed) to reach the entire top and bottom surfaces.
To dust, use a soft clean cloth or chemically treated dust cloth and tilt the slats as above.
To wash, use a damp cloth or sponge and mild detergent. Use warm or cold water - NOT hot water. Tilt the slats as above. Protect the floor or sill from excess water. The blind can also be taken down, placed in a bath tub of mild soapy water, then rinsed clean, wiped dry, or allowed to dry completely in the open air.
Care must be taken when cleaning real wood blinds. Washing the blind is NOT recommended. Although the wood is sealed, water or even excessive dampness may cause warping or discoloration of the slats. Since the surface of the slats is smooth, dust may be easily brushed off at regular intervals using a clean soft dust cloth or a vacuum cleaner brush attachment. Clean them as described above.
Fabric Pleated Shades:
Most of the cellular shades, like the Hunter Douglas Duette shade, are anti-static, and they require very little cleaning. A light sweep with your vacuum cleaner brush attachment is all that is needed to keep them dust free. For a more thorough cleaning, the entire shade assembly may be gently wiped with a soft damp cloth using lukewarm (not hot) water. Take special care when handling opaque (blackout) shades to avoid creasing, and do not immerse them in water. For tough stains, spot clean with a mild detergent. Some shades, like the Graber Crystal Pleat have a "soft hand" fabric. Be very careful when trying to clean these types of shades as they tend to "split".
There is an assortment of custom made products for cleaning window blinds.
You can also consider using a professional window blind cleaning service.