Here are my ideas so far:
At night, go to the billboard you want to take down. It will probably have a power cable running up the side of it, to power the lights. Cut that cable.
Now that the lights are off, set up your stepladder, so that you can reach the elevated ladder on the side of the billboard. Climb all the way up.
As far as I know, the actual "bill" itself is just a piece of cloth or tarp draped over the board. So, it seems like you should be able to cut it. I would use normal scissors to cut away the bottom part, and some type of long-reach pruning shears to cut away the sides. Not sure what to do about the top - maybe a few good yanks would take care of that (but be careful that it doesn't fall on you, and knock you off the catwalk). You could also try setting it on fire, but that seems way too dangerous to you, and the fire might spread to other things you don't want to catch on fire, like a nearby forest.
Does anyone have any better ideas on how to do this?