Step 1: Let's Make Something.
Step 2: Take It Apart.
Step 3: Pull the Skin Off.
Step 4: Oops! Don't Rush! Think First.
If it happened just use sharp tool to separate them and save filter to put it back later.
See wiki for details.
Step 5: Get It Cut.
Sand face and back sides of plastic plate with fine sandpaper to diffuse light then cut notches on sides of plate where you plan to install LEDs.
Shape of LED should be formed with file to fit into the notch
Step 6: Let's Practice Some LEGO ;-)
You can use hot glue to secure it on place.
Step 7: Let's Give It a Trial...
Step 8: Bring All Bunnies Into the Cage.
-white sheet of paper to reflect light back;
-polarizing filter (if you removed it by mistake);
-plastic plate with embedded LEDs;
Be very careful with golden pads on PCB and elastomer connector (zebra strip). Use pure alcohol to clean it if you touched contact pads with your fingers.
Another important thing is proper alignment.
If after powering it up you got missing lines (characters) on LCD then connector has shifted from original position. Carefully take it apart and re-align it.
Step 9: Final Step.
So, solder it up.
There are two points to get power to LED from.
You can connect it directly to logic power supply (pin 0 - GND, pin 1 - 5V) of LCD.
Or you can make separate connection(on my LCD there were unused pads for optional backlight) and in that case you'll be able to use PWM signal to control brightness of LED.