Before you start working on any laptop or notebook computer, remove the battery. It's just too easy to accidentally power up a laptop when you're working on it, and that could easily spell disaster, even if you don't panic.
The first part of the puzzle when you repair a laptop screen is to determine what the failure is. We aren't going to do that here, because there's actually nothing wrong with this Toshiba notebook, I'm just using it for example. The second step, once you know what you're trying to fix, is to find the screws to take apart the cover, which houses the LCD and inverter.
Most Toshiba laptops use four screws to secure the plastic bezel, two at the top and two on the hinges.The top screws are hidden under some rubber bumpers, you really need to dig a screwdriver with an edge on it into the side to compress them enough to get them out. The screws below the LCD on the hinges are under rectangular paste ins that I needed a jewelers screwdriver to pry up.
I don't have any particular order for doing this, so I started with removing the backlight from the top of the LCD. The backlight is secured to the LCD by two small screws that do require a jewelers Phillips to remove. Laptop LCD backlights are actually florescent bulbs, with CCFL (Cold Cathode Fluorescent Lamp) being a favored technology.
The average life for a laptop backlight is on the order of 30,000 hours, or more than three years of 24 hour a day use. When the backlight in a laptop flickers or fails, it's more likely the inverter than the CCFL tube.