The first thing to do is to check the laptop package to ensure it guides, CDs and components that should be there. In particular, check to see that essential cables are all in the box.

Check your laptop package contents first

The next thing to do is to check your laptop's exterior. Check the front, back, top, bottom and sides to ensure that there are no dents, scratches, etc. If you detect any, then you should return it back to the manufacturer and ask for a replacement.
 

Ensure the laptop's exterior is fine

Boot up the laptop and check for any "out of the ordinary" messages during the boot-up sequence. Hopefully, there is no weird message - if there is, you need to contact the manufacturer immediately.

The next thing to check in a new laptop is to ensure that the hardware is in line with what you ordered. If you're a Windows user, right click My Computer and select Properties. Check that your CPU information is correct. You should then select the Hardware tab at the top of the dialog box and click Device Manager. Check the list of hardware listed by Windows against the items you ordered in your receipt.

The keyboard is something users usually fail to test. You should open up notepad and test out every key on your keyboard. Don't skip any keys - I've sometimes owned laptops for months only to realize that an infrequently used key is faulty.
 

Check that the laptop keyboard is working fine

The ports and connections on your laptop are important components. Make sure you check that the DVD tray, fingerprint reader, USB ports, Firewire port, Bluetooth, video output ports and printer connection all work normally.

An important check that you need to do is to scan the laptop screen for dead pixels. You can do this with some help from a program called DeadPixelBuddy. If you spot any dead pixels and they are above the limit specified by the purchase policy, you have the right to return the unit to the manufacturer and get it replaced.