It is important to offset the painting from the wall, so that the LED strip has a place to sit as well, and has sufficient space for the light to leak out.
On the back side of the frame, install 4 screws at each corner, about 1 inch from the edge of the frame. Leave enough of each screw end to string the strip around it (about 10 to 15mm depending on the screw head and any loose canvas that my interfere). Finetune the screw lengths by hanging the painting, pressing on each corner in turn and checking for a wobble. In a way the whole assembly should be like a table with four legs -- it should not wobble.
Secure the LED controller module and 12V power cable so that the power cable exits the frame on the lower middle edge, to go to the power supply plugged into the wall. You can use safety pins and attach to the loose canvas at the back that had been wrapped around the frame, or any other means available. You need to have enough tension for the strip so that the lights point outwards. This can be done by securing the power end to the frame, going around the screw corners and setting up a small loop at the other end by using the adhesive backing. You don't want too much tension (as that can damage the strip), or too little (as the light may not be uniform). It is important to cut any excess LED strip length in a suitable place (in this case I only used about 3m out of the original 5m strip).
Rev 18 July 2016:
Did the second painting today.
What I wished for today was to get some rigid L shape pieces to mount the strip on under the frame, although it looks like I will never make the time to go to the hardware store any time soon; maybe in the next iteration.
Back in mid 2016, when this project started, getting a quick win was the priority. It was worth it! In everyday life, these lights proved to be practical for their functionality, with a dimmable remote, as well as providing a wonderful relaxing evening atmosphere. However, it was always a longer term view to install these lights properly on a rigid structure.
The advantages of this higher quality finish include: 1) improved illumination uniformity via diffuse white channel, 2) preventing twisting and sagging of the LED strip, 3) improved mechanical resilience against bumps and handling.
The following illustrates how I installed PVC moldings to the frame.