Turn the coffee table upside down onto a soft surface (carpet or blanket) to protect it from scratches.
Locate the coffee table's assembly hardware. It's usually at the top of the legs or in the frame directly under the tabletop. Find the screws or bolts and that hold the tabletop onto the legs or frame. Bolts will have nuts or wingnuts.
Unscrew the screws or use a wrench to remove the nuts and bolts. Use pliers on tight wingnuts. Remove all the hardware holding the tabletop on. Put the hardware in a bowl or other container. If the coffee table has individual legs, take the legs off one at a time and place them on a soft surface. If the tabletop is attached to a frame, lift the frame off of the tabletop once you have removed all the hardware. If the frame is heavy, have an assistant help. Move the frame clear of the tabletop and set it down.
You can now lift the coffee table's top.