1.) Open up GIMP. (Obviously)
2.) Open the picture you want to have a beam around.
Like so:


3.) Add a new layer.


Here's what the new layer should look like:


4.) Select the "Paths tool."


5.) Create a path around your pic, curving where necessary. (This part takes practice.)

NOTE~ Make sure you are on the "new layer!"




6.) "Stroke path." Make sure you use the paintbrush.





This is how it should look so far:

7.) Go to "Filters", "Alpha to Logo", then "Neon."

\
Here's what the neon screen should look like:

8.) Choose your color. "Glow color." (I'll use pink.)






Here's how it should look:




9.) Delete the black layer. Merge the "neon tubes" and "neon glow."


10.) Use the eraser and eraser every other line. Make sure you're on the "neon glow" layer.

11.) Merge layer down.
12.) Save.

Here's the result!


Hope this helps!
Post here if you need any further help and post your results!

I'll post a better example in a second. xD