Major Pain! We switched to wooden blinds because our 2yr old kept breaking the slats and my husband was using duct tape to fix them.
The way I would clean them is take old socks and put them on my hand. I would grab the blind so it would clean the back and front.
Sometimes I would use a little cleaning product in water to clean really tuff spots. When I was finished, I would toss the socks in the washer for next time.