How do you clean cast iron gas stove burners?

I don't know if this is right or wrong, but I put mine in the dishwasher.

Hot soapy water in the sink. You can also clean in the dishwasher if they are fully coated in enamel! ( source)

http://www.howtocleanstuff.net/how-to-clean-cast-iron-burner-grates/

ditto the dishwasher. a bit of steel wool if they appear rusty to remove the rust.

Soak in the kitchen sink (lay an old dish towel on the bottom of the sink), with a squirt of dawn dish soap, a cup or two of white vinegar and a few heaping tablespoons of baking soda if they are really grimy. If not bad, an hour or so is fine, if really yucky, do it overnight.