You'll need to take the individual pieces down, hand wash and dry them. While they're drying, you can clean the metal parts of the chandelier. Good luck!
You can wash each crystal with isopropyl on a cotton ball.
Patiently! I used hot water and ammonia. Wipe each crystal with a wet washcloth. Wipe the dust off the metal arms also. It's tedious, but will be oh, so beautiful when you get done! Here's my family's old dining room chandelier we hung in my daughter's bedroom, and what I did to update it a little: https://lorabloomquist.com/ways-to-update-a-vintage-chandelier/
my mother in law use to take her crystals downs and put them in the dish washer. They came out great!
Call your best lighting store--there is a product you can spray on --you put a drop cloth or old washable/throwaway spread underneath to catch drops--spray it well...it cleans every piece--the hanging crystals will drip off all dust and grime--no streaking or blurry looks--I am sorry I cannot remember the name but any high end lighting place will know it.