You have the same carb I do, and I know how to adjust it.
Different manufacturers have different carburetor setups. From Pianoman's description, it sounds like he has the same carb I do.
Tom and Tirebiter are correct for this particular carb.
The only adjustment screw that my carb has is the idle screw. That's it.
The push-button looking thing is called a "tickler". I have an old Moto Guzzi motorcycle that has the same push-button ticklers on the carbs. Their only function is that when you hold them down for a couple seconds they slightly flood the carburetor on purpose to help it start when it's cold, but I never use mine, and actually plugged it with a screw to eliminate a possible source of leaks. (In case you are curious, they work like this: The button is connected to a pin that goes into the carb. Pushing the button pushes the pin, which pushes the carb float down. Pushing the carb float down makes the carb think the bowl is not full yet, so it pours more gas into the float, thus overfilling the carb. Holding this button down too long will cause gas to start leaking out through the button.)
Adjusting the mixture is pretty easy. Unscrew the cap on top of the carb where the cable goes in. Pay attention to what it looks like when you are taking it apart. The washer with the slot in it goes OVER the E-clip when you reassemble it. Compress the spring, unhook the cable from the sliding cylinder, and take the needle out of the assembly. On the needle you will see 4 grooves. Putting the E-clip on the top groove lets the needle sit lower into the carburetor, which blocks the fuel flow, which leans out the mixture. Putting the E-clip on the bottom groove gets the needle up out of the way a little, which clears the way for more fuel to go through, which enriches the mixture. Top groove = lean. Bottom groove = rich.
I live about 3 miles from the ocean, which pretty much puts me at sea level. I find that my bike starts easiest and idles best with the E-clip on the second groove from the top. The top groove makes my bike harder to start and the bottom two grooves make it so rich that it spits a lot of unburnt fuel out of the tailpipe.
If you are at a high altitude, I have heard that you can get a new jet (the nozzle that sprays the gasoline) to adjust for altitude. Changing the jet would be really easy, but figuring out which one you need might be a pain. Hopefully you won't have to do this. Mine runs fine with the stock jet, so I have never had to mess with it.
Anything past carb adjustments might be some other engine stuff, so let us know what kind of problems you are having and I'm sure somebody here can help fix it.
So to sumarize:
The only thing the screw does is set your idle. Screw it in to make your bike idle faster, screw it out to slow the idle down. This screw will not affect anything else on your motor except idle speed.
The only way to adjust your mixture is to move the E-clip up and down the needle. Since it works so well for me, I'm going to suggest starting with the second groove down and work from there.