A flickering laptop screen stems from the backlighting of the display turning on and off. This can result from multiple factors, but the most common cause is the wearing out of the backlight inverter.
For the easiest way to test this possibility, hold a flashlight against the screen while it flickers. If you can still see your screen in the light of the flashlight, the problem lies with the backlight and not the LCD itself.
Before you begin, locate the model number on the base of your laptop and search the Internet for "Dell Latitude [model no.] service manual." Dell publishes many of its laptop service manuals online, and having instructions to guide your disassembly will save you time and headaches.
If you have a camera, take pictures of every step of the disassembly before and after you do each major step. Having the pictures to see how parts should go together will make the process much easier.
Use a screwdriver to partially disassemble your laptop. Using the service manual, take apart the screen assembly enough to allow you to remove the screen bezel and expose the backlight inverter board.
If you do not have access to the manual, start by searching for any small plugs or pieces of plastic that might cover the screws holding your laptop's lid together. (Screws might sit under the little rubber feet around the screen as well.) Check everywhere around the LCD for potential screws; the plastic around the LCD is thin, and if you attempt to pull the screen apart while it remains screwed together, it will snap. Once you have all the screws, grip the plastic front of the screen near the LCD with your fingertips and "roll" a portion of it away from the screen. The plastic bezel on an LCD attaches with plastic latches, and rolling from the inside of the screen to the edge should release them. Once you have the bezel off, look for the backlight inverter—a small circuit board with a socket on either end. It usually sits just below the screen in the lid.
Unscrew the inverter board and carefully disconnect it. Plug in the replacement board, place it back in the correct location and screw it down.
You might wish to test the new board at this point by plugging in the laptop and turning it on. If you do so, be very careful: The inverter produces potentially painful or even dangerous high voltages.
Press the front screen bezel back into place. The lid should fit securely together when reassembled and should come together with a "click." Check to ensure that you have reattached all the latches before screwing the lid back together. Reattach any plugs, rubber feet or other screw covers that you removed earlier.
If you didn't test the laptop already, plug it in and test it. You should have a fine and flicker-free picture.