first off remove your chain and soak it in wd-40 in a glass jar. you can leave it in there from 1/2 hour to over night.
just a note. wd-40 is a degreaser. do not use this to oil your chain.
give the jar a few swirls for more cleaning action. like the washing machine. you can even make that sound if you like....
then you must brush the chain with a nylon brush. i use old tooth brushes as they are small and cheap. make sure you take your time and get in all the nook and crannys. do this systematicly so you don't miss a link. both sides as well. try not to let any wd-40 go down the drail. its bad for the earth.
rinse in the jar again and then pull the chain over your hand to find any stuck or binding links. these will slow you down and break on that spot.
dry the chain thoroughly.
i like to use a dry lube with some wax. since i clean and lube my chains alot, i use a cheap one. as long as you keep it up this is fine. a wetter wax and/or oil will do a better job, but will have more sand/dirt stick to the chain and that will be worse.