There are a wide variety of chandeliers out there from glass to plastic.
In most cases you are able to remove the individual pieces, clean by using a good terry cloth and water or window cleaner.
You can make your own mild window or glass cleaner by mixing 1 gallon of distilled water and a cup of rubbing alcohol and a tablespoon of dish soap. Mix in a gallon jug and pour into a clean spray bottle.
Polish dry the pieces with a terry towel as you clean to prevent residue Using distilled water will also reduce and residue). And work in small sections so you remember where all the pieces go.
In a Hurry
Use cotton gloves and just run your hands over the pieces for a quick cleaning (you can lightly spray your gloves with a cleaner.)
You can also use a feather duster (osterage feather dusters are best, or a can of compressed air for a quick dusting.
If your chandelier is glass then place a comforter or quilt under the chandelier as you are cleaning to catch any flying pieces and prevent or lessen the chance of breakage it also will act as a drop cloth when you are cleaning. Be sure you are working on a stable surface a ladder is best as you can move it as you move around the chandelier, in some cases where the chandelier is above stairs etc. proper scaffolds should be used.