I'm not an expert but can speak from experience, having worked on pretty much every single popular carb out there ranging from the Mikuni VM and BS series to Keihin flatslide to the Solex and SU carbs found on Fiats and Dolphins, the Jikov and Pacco found on Jawas, racing carbs on karts and formula cars etc.
Carb tuning is not a simple subject and requires lots of theoretical knowledge as well as excellent feel for what your particular engine does under different conditions (by this I mean how it sounds, how it runs, how it pulls, transient response, how it slows down, how crisply it revs in neutral etc). I would say that tuning a performance engine for the street is among the toughest things one can do, even more difficult than tuning it to run on a racetrack!
I won't go into specifics, but almost always you have to start with good spark plugs that are properly gapped (preferably new), the best quality fuel you can get, and good quality two-stroke oil mixed at the correct ratio, if the engine is a two stroke. The air filter has to be clean as a whistle - if you don't take care of these things first, any misfires or other poor running can never be traced to its true origin, and this may not necessarily be caused by the jetting.
Next thing you should do is read up very well on carb theory. There are many good automotive engg. books that explain this very well. Reading on the internet is spotty because any idiot can write anything he wants - takes a bit more effort and credibility to publish a book!
After that, the important thing is to get hold of a workshop manual for your bike or engine and read the heck out of it. You need to understand EXACTLY what each adjustment does. Generally every adjustment on the carb is for a specific range of throttle opening. The idle and air screws that are on the outside of most motorcycle carbs, together with the pilot jet inside the float bowl control the first 25% approximately of the throttle opening. The needle position, needle taper and the shape of the slide control about 25 to 75%. The main jet controls 75% to WOT (wide open throttle).
Before beginning tuning, the important thing is to open and clean the carb thoroughly. Here in the US it is easy because you can buy pressurized aerosol cans of carb cleaner - just point and spray in any hole and you're done. If this is not available you can just use clean petrol and a toothbrush to get rid of most deposits - then blow well using your lungs. The workshop manual usually has a procedure to set the float height which is extremely important because it controls the mixture throughout the full range. Learn how to set this properly using the manual - many times it will call for the use of a special tool but they usually also give a measurement from some surface on the body of the carb - its easy to measure using a ruler. Also check that the float needle valve is not worn out and leaking. In race engines we do different things with the float level to suit the track but this is not required most times for a street engine.
Its very important to make sure that the carb is completely restored to the same condition it came from the factory.
The typical tunable parts that you can have on a motorcycle carb are:
Main jet
Pilot jet
Needle
Emulsion tube (the part that the main jet screws into)
Slide
Venturi (if removable)
You can get to 95% of the perfection in jetting with just proper selection of a pilot and main jet, needle, needle position and adjusting the mixture screw. Most of the guys here will probably not experiment with jetting to a level where a slide or venturi change is required.
A two stroke is a lot more sensitive to proper jetting and therefore much easier to read. You can tell a lot just looking at the color of the plugs and the way the engine picks up and drops revs. A typical "plug chop" involves running the engine at the throttle opening that you are trying to adjust (i.e. main jet adjustment needs WOT runs) and then shutting off the engine and coasting to a stop. Pull the plugs and see the color around the outer electrode (called the land) and of the insulator. If it is oily or black, you know its rich. If its white and has specks of aluminum you probably melted something inside the engine and need to richen it out. If its a mild to medium brown or golden color, you're doing it right. On a street engine that will see different weather conditions, different qualities of gas, different loading etc. I would not go too lean even though the engine feels awesome when it is on the edge and close to a complete meltdown.
Different people do different things but my preference is to use whatever it takes to get the engine started and running decently (not great but decently). Then do the main jet calibration. You have to find a deserted piece of road to test full throttle acceleration. Start big and then keep reducing until the engine pulls hard, but you have to be careful: do a plug chop everytime. Multiple sets of plugs will be required during main jet adjustment.
Once that is done, 50% of the work is over since you dont have to take the float bowl apart everytime to change the main jet (some carbs have separate fittings on the bowl to make this easier). Next, move on to the needle. Needle selection is not easy, but it is if your choice is limited

. Start with the needle in the highest position (i.e. lowest slot) and keep reducing until you get very crisp acceleration at between 1/2 and 3/4 throttle. You have to play with mixture screw (the one that's on the outside of the carb) adjustment at the same time as needle position adjustment, in order to get the crispest response between 1/8 and 1/3 throttle.
Next is the off-idle and idle adjustment which is again an iterative process between the mixture screw and idle speed screw. Generally the crispest throttle response for spirited driving is not obtained at the manufacturer recommended idle speed - they do it for emission and fuel economy reasons. You may have to go a little higher and when you are done, the vehicle will take off very crisply from off-idle and transition to 1/2 throttle in a very smooth manner.
Sometimes the pilot jet size needs to be finely adjusted if the engine response is not as crisp as desired. It takes a lot of experience to reach this stage unless the carb is from a completely different engine.
So like I said in the beginning, it takes a lot of time to learn carb tuning skills but its not hard. It just takes a lot of experimentation and discipline on your part (i.e. keep notes of every adjustment you make, and the results) to achieve anything useful. Take it to the mechanic if you don't want to put in the time!