d'oh, screenshot made me think building above ground and made me forget what I had just read.
Digging vertical pillars is really easy.
Code:
for i = 1, <height> do
turtle.digDown()
turtle.down()
end
for i = 1, <height> do
turtle.up
end
Digs straight down then comes back up to where it started.
Digging a circle is actually kinda complicated since your circle design would either have to incorporate the blocks the turtle has to move through outside the desired circle, or the turtle would have to fill in holes behind itself. Filling in would probably mean you'd have to code a way for the turtle to know when it's digging the circle and when it's digging to get to where it needs to be to keep digging the circle. It's certainly possible, but it's probably easier to hollow out the majority of your cylinder with some sort of quarry (a turtle using the default excavate command would be fine) and then do the edges with a series of shafts. It only takes about a minute for a turtle digging straight down to hit bedrock (maybe 2 minutes if you start at the top of a mountain?).
Most of what I know of LUA I learned in a few hours watching Direwolf20's CC tutorials and reading
http://lua.gts-stolberg.de/en/index.php and giving myself assignments to utilize each new bit of info. After that, I've just learned by seeing something in another turtle program I'd like to try. That's been enough for me to write my own quarry programs (although they're nowhere near as good as what's on the CC forums) and handle various tasks around my base like auto-enchanting.