For the bed frame, simply attach the LED light strips to the underside of the frame rail that sticks out from the side of the bed. Put all four strips in series as per the instructions, hiding the cords, power modules, and switches as you see fit. Finish assembling the bed frame as per the wonderful pictorial instructions IKEA provides. For the nightstands, use one kit, putting one LED light strip under each projecting shelf-thingy and connecting the two strips in parallel using the supplied wiring, again per IKEA instructions. Then finish assembling the nightstands and attach to bed frame. When you're done, switch everything on and your bed should look like mine in the photo. You can see the cords and power supply on the floor. At some point I'd like to hide all that mess, and make up a slick control system with hidden switches on the nightstands and perhaps a dimmer circuit. The numerous excellent LED instructables should make this an easy task.
I did pretty much the same thing you did, only with RGB LEDs and a color changer. Check it out: http://www.youtube.com/watch?v=YzNJM7Djn-c
http://www.ikea.com/ms/en_US/customer_service/assembly_instructions.html