Ah,,,yes. adjusting a carburetor in three thousand words or less. Haha!
Well, on the 031 you start by adjusting the Hi and Lo jets to 1 and 1/4 turns out from closed. Just turn the jets clockwise until there is a noticeable stop. Don't crank them down tight or you risk ruining the jets. Then back them out to about 1 and 1/4 turns. That should make the saw run. You may have to adjust the idle speed screw as well to make the saw idle.
After that, you have to adjust the Lo jet in either direction to make the saw idle well, and accelerate with a snap. If it hesitates or bogs as we say, you don't have it right. You should be able to find a sweet spot.
Then to adjust the Hi speed jet, rev the saw to wide open throttle. This is hard to describe at this point. You want the engine to rev up with a smooth sound, and then when it reaches full revs, it should immediately sound rough. This is called four cycling. The best way to test it out is to run the saw in a log. When you run the saw in the log it should sound like it is running smooth, but when you remove the bar from the cut, it should sound like it is sounding rough and maybe like it has lost some revolutions.
I think you need to use the search function for a better description, as there are untold threads about adjusting the carb on this site.
One of the AS sponsors called "Madsens" has detailed information and videos on adjusting carbs as well, and it would be a great place to hear smooth running two cycling, and rougher running called four cycling.
The 031 is easy to hear normal two cycle smooth sound, and the different sound of four cycling. If you have the Hi speed jet adjusted too lean you may fry your engine. If it is too rich it will four cycle in the cut, and the saw will not develop maximum power, but you won't fry your engine in the short run.
Bob