Sit on the mattress and bounce; narrow down the location of the squeaking.
Remove each squeaky screw in turn. Wrap the screws with plumbing sealant tape and thread a plastic washer onto each one. Replace and tighten with a screwdriver.
Spray a bit of silicone-based lubricant onto any squeaking bolts or rails.
Cut a piece of felt into a square the size of the spot where two sections of frame meet and squeak. Cut screw-sized holes in the center of the felt, remove the screws and place the felt between the two pieces of frame. Insert the screws through the holes in the felt and reassemble the frame. The felt can also be placed in between slats if the squeak is coming from that area (not near the screws).
Place rubber furniture cups or an area rug beneath the bed legs if the bed rests on hardwood floors.
Center the mattress and box spring on the frame to eliminate squeaking caused by improper weight placement.