Assuming the LEDs have the proper resistors/circuit built-in, the biggest problem will be wiring them to the door switches. Some cars have this switch as "switched ground", others switch the hot - a visual inspection of the switch's wiring scheme or a meter will be able to tell you what's what. For the switched ground type, simply wire 12v to the + lead of your LED circuit and attach the ground of the LED circuit to the door pin switch.
For the trunk, you could add a pin switch that will do the same as the doors. Or, attach a mercury switch so that it closes when you open the trunk. Or, just a simple manual switch works too.
If accessing the door switches is difficult, just find the right wire in the kick panels. Look up your car's year, make, model somewhere that has car wiring diagrams for auto security installations. A quick google search came up with this:
http://www.bulldogsecurity.com/bdnew...ngdiagrams.asp
Also,
http://www.the12volt.com/ has pretty good resources and diagrams to help you out.