Small two-stroke engines, to make them lightweight and affordable, do not have an internal lubrication system as other engines do. To make up for this, oil is mixed with petrol. The engine gets it's internal lubrication from burning this petrol/oil mixture. This is important to remember when tuning one because if you tune it to run too lean on fuel, it's also running too lean on lubrication. Put another way, when you tune the carburettor, you're not only making it run properly, you are also making it lubricate properly, protecting the engine from damage.
Check the air filter. If it needs to be cleaned/replaced, do this first.
Back the idle adjusting screw and high speed adjusting screw out two full turns.
Warm up the engine. Don't worry about running it out of adjustment. With the adjusting screws backed out the engine will get too much fuel, but it should run.
Set the idle. With the engine idling, turn the idle screw in clockwise until you find the spot where it idles best. From this position, turning it in either direction should cause the engine to not idle as well.
Set the high speed screw. Rev the engine to full speed and adjust the high speed screw until it runs it best. Then back it out 1/4 turn, this is to protect the engine from running too lean.
Use it for a while, then check to make sure the adjustment is okay. Do this by removing the spark plug and examining the colour of the end that goes into the combustion chamber. A light brown colour is best. Darker means it's getting too much fuel and should be adjusted. Turn the high speed screw in clockwise just a little. A lighter colour, especially if it's white, means it's getting too little fuel and can damage the engine, readjust immediately.
These instructions are for small two-stroke engines. Like those used for leaf blowers, weed eaters and lawn mowers. Adjusting two-stroke motorcycle engines will be similar but more complicated.