How do I stop a bed frame from squeaking?
I fixed my metal bedframe by putting leather patches between parts that are rubbing.
Wooden frame is a bit more tricky - not so easy to identify where the parts are rubbing, but this is the first initial step. 
I'd say check all the joints and see if you can tighten the bolts or add glue to moving parts.

Basically, the noise comes from parts rubbing on each other. If you can eliminate rubbing, or put something between the rubbing parts - that would reduce the noise.