1. First, you need to identify the problem. If the screen flickers, or initially comes on but then goes off, or an image appears but extremely dimly, it could be the inverter that drives the backlight that’s failed. If so, go to Step 3.
2. If the screen is totally black, or perhaps shows garbage, attach an external monitor and, if necessary, press the appropriate key to switch to it. If you get no image on the monitor it’s probably the video circuitry so replacing the screen won’t help. Unfortunately, it looks like you’ll have to buy a new laptop.
3. First, as a safety precaution, both for the laptop and yourself (bearing in mind that there are high voltages in a laptop, despite it being powered from a low voltage battery), disconnect its charger and remove the internal battery. If you have one, wear an anti-static band which is earthed. If not, earth yourself by touching a radiator or any other metal object that is grounded.
4. The screen bezel is sometimes secured by screws hidden behind rubber covers. If so, remove them using a very small jewellers’ screwdriver. Now remove the screws. As you proceed, keep each set of screws safe and separate, making a note of where they fit.