Debugging with a multi-meter

I have not used a multi-meter before and it is one of the basic skills that I need to learn. Handily it also helps me get to the bottom of the issues with the LED Display kit that almost works and with some work I can debug the circuit.

I hadn't a clue where to start, although I already had a cheap M-830B multi-meter from Maplin. Thankfully this helpful gent created a video on multi-meters here which gave me the basics I needed to get going. I am only using the LED test section of the system at the moment as I want to work out why the LEDs are not working.

Following the traces in the PCB I can see that the LEDs all connect their negatives to the same line and that by testing the LEDs one at a time on the row I know they all work, so I have looked at how the current is passing down this line and it looks as if one of my bodged soldering points has stopped the flow. Now I need to un-solder the LED and try and find if this section of the PCB can be saved, or what I can do to fix or bodge around it.