Remove the mattress and box spring from your bed to expose the frame.
Wiggle the bed a bit and watch the frame to determine if something is loose. If there is a major issue with the frame, like a loose side, you will be able to see it clearly.
Remove and tightly replace the screws in the frame individually. If your bed frame is metal, wrap a piece of sealant tape around each screw or bolt. If the bed frame is wooden, scrape the threads of the bolts over a bar of soap to pack dry soap between the threads. Place a new plastic washer over the existing washer before screwing the bolts back in place.
Look at each joint between the wooden sides, if your bed's frame is made of wood, and apply wood glue at the loose joints. Hold them in place with C-clamps until the glue dries.
Push on your mattress and box spring while they're still off the frame. If either are squeaking, replace them.