Are there any simple steps one can follow to verify if a notebook is clean from hardware spyware?
No. Simple steps can only identify simple attacks, especially if the investigator is not familiar with computer hardware. Planting a hardware device for surveilence or reconnance is a very sophisticated and costly attack.
What should be looked for? How should it look?
I have never seen a laptop, notebook, or any type of device that had hidden surveilance hardware inside it. I dont know of anyone in the IT Security community who has seen such hidden spy hardware in a computer. And I was unable to find a recorded criminal investigation where a piece of spy hardware was hidden in a computer.
That said, to investigate a computer notebook you will have to be an expert in ASICs (Application Specific Integrated Circuits), printed circuit boards, printed wiring assemblies, computer data buses, FPGA (Field Programmable Gate Arrays), schematic diagrams, wave soldering, reflow soldering, and manual soldering.
I would start with the service manual for the laptop. Read the manual and find all the place there are screws to extract. Look at those areas for evidence that a screw has been loosened or removed. Evidence could be: scratches or dents where the top of a screwdriver hit or rubbed against the case, the screw being at the wrong depth compared to an identical screw, slight oil or graphite residue. Then look for small opening where something could be inserted into the laptop without taking out the screws. These are things like: air vents, PCMCIA slots, speaker vents, a removable CD/DVD-ROM drive, the security cable slot. It is helpful to photograph these areas before you do anything to the laptop, so that you can send the pictures to others to look for signs of intrustion.
Then remove all cables and components from the laptop. Next remove any components that do not require you to remove screws to take them out: the battery and often the CD/DVD-ROM drive. As you go examin and photograph each step. Next I would remove the hard disk and RAM. Those usually require the removal of screws but are otherwise easy to remove.
Next I would go for the screen, take off any pieces you need to detatch the screen. I would look for a hidden device near the base of the screen where the cable comes in behind the screen. A hardware spy device will either need to come with its own power or use the computer's power. If it uses the computer's power it will need to be near a wire or cable carrying power. It would be small and similar in color and markings to other chips.
Then I would check in the main case. Again it is likely small and connected to a power line or cable. It might even have its own ribbon cable of small board to make it look like an intentional part of the design.
Your best chance is to compare the parts against the service manule and find something that isn't in the schematic or diagram, or more likly something that is a little bigger or a little out of place.
Speculation on the device:
What data is it ment to capture? Maybe audio, maybe video, maybe both. It likely would not be data that is stored on your computer. Data stored on your computer is easier to acces by other more common attack methods.
So why audio or video? Maybe your laptop does not have a built in microphone or camera. Or maybe the intent is to be able to observer or listen in multiple dirrections at once. The laptop can only be a platform for power and data transmission. These types of device in the past had to have their own RF to transmit, but with the data transmission of the laptop any extraneous RF transmission would just expose the covert device.