One thing that I forgot to mention that I likely should have-don't think the pilot circuit only affects the bottom end.There is a fair bit of crossover as you increase the rpm's and head toward the mid.For instance,as you start accelerating from idle toward the mid,your pilot still has an effect but it lessens as rpms increase and you start coming into the mid.A pilot circuit that is misjetted therefore,has a fair effect on your low to mid transition-hence the response issue.
Now then,Kawi 250,the initial post is the best way to be precise but if you want to play around a little and get a feel for it,that's not a bad idea either.
With the bike shut off,put a little paint or marker mark on one end of the slot in the airscrew then a corresponding one on the carb body.After that,turn the screw to the right(clockwise)counting turns as you go(ie 1/4,1/2,/3/4,1,11/4 and so on) until it LIGHTLY stops-don't force it.From there return to your original position.Ideally you should be in the 1 to 2 turns out range(if not,don't worry about it).Start the bike then warm it up fully.Once you've done that,turn your idle down so it's just idling if you were higher than that.
From here you can play around with the airscrew all you want as you won't hurt anything.
Once you change the airscrew setting,it will take a few seconds for this to become noticeable so rev it up a couple times and then let it settle down for a few seconds.
To get a feel for a rich setting,turn your screw about a 1/2 turn out from seated,start the bike and try it.It has sort of a "heavy" sound and feel.Ride it a bit this way starting from a stop and slowly accelerating,then try it accelerating normally.Once you get a feel for that,turn the airscrew about 2 1/2 turns out(leaner) and try it again.
This will give you a feel for both extremes.
From there,adjust it 1/4 turn at a time or so between these settings,ride it from stopped while mildly accelerating,then quickly accelerating and keep repeating until you get to the best setting for power and response.
Once you do,shut the bike off and count the turns again as you turn the screw in clockwise.Once you have a number,return it back to that setting and let us know what your number is and we'll tell you where to go from there.If your best results are farther out than 2 1/2 or farther in than one you have a little jetting to do.Fun,fun and there's power to be had,and you can tune it yourself.Who could ask for any more than that