This link should help you out:
My mom would have us do it every summer. She would put them in the tub with cleaning solution and bleach. She would wipe when in the tub with a sponge or a rag. Then we would dip them up and down in the water. Once done she would let out the water and let them lean in the tub to get rid of water. Once drained we would put them back up.
You can buy a cheap tool at WalMart (under $10) that is microfiber with multiple "fingers" that go between the slats. Then dampen and run end to end. Repeat until all sections are cleaned.
I'm with Dollene but use powdered DW detergent dissolved in very HOT water enough to cover the slats. Drop them in swish around to separate the vanes and let them sit overnight. In the morning swish again, drain and rinse then let dry. this works great for blinds as well.
we have rental property so you can imagine what some things look like after tenants move out.