Ahh, yes carburetors. Everyone is so afraid of carburetors. I've heard people refer to carb problems as "motorcycle cancer," as if to imply that "once the carbs start to go, your bike is basically fucked." Even though carbs are the most common cause of running problems, nothing about them is irreplaceable or unfixable.
The worst set of carbs I have ever repaired came from a 1978 CB750. The bike had been sitting in the rain for 25 years. The tank was so rusted that I just pushed the top down and it all caved in. The carbs were completely seized, full of black sticky gas and rust. However, after careful cleaning and diligence and attention to detail, they were soon back in serviceable condition, and the only parts I had to replace were the float bowl gaskets. So, if your carbs are in better shape then that, they can definitely be repaired!
Here is basically how they work. Gas flows into them via one or two fuel lines, and is dispersed amongst each carb. From there it flows past the float needle, which opens and clsoes as a result of the raising and lowering of the float. If the float is sticky or these components are dirty/worn, you may get fuel starvation/flooding issues. From here the gas pools in the float bowls. These bowls may leak if they are loose or the gasket is installed improperly. These gaskets are hardy tho and can last for decades.
The pooling gas waits to be drawn up the jets via the vacuum of the engine. These jets clog easily, just one grain of sand can do it. This is why it is so important to put in a good inline fuel filter. More gas is drawn up through the main jet when the slide needle rises. Depending on the design of the carb, it can rise either via direct linkage to the throttle, or more commonly these days, they rise on their own when more vacuum passes through the carb bodies, this is called Constant Velocity or CV carbs.
The slides need to operate smoothly in order to move up and down in a predictable fashion. Also, they have a spring on top which pushes them back down and resists the vacuum so they don't open too quickly, as well as a diaphragm which maintains a little pressure. If the diaphragm is damaged or installed incorrectly, the slide will rise too quickly.
Carbs also have a choke circuit, which can either add more gas or reduce the amount of air, or both. This helps the bike start when it is cold. The motorcycle needs atomized gas in order to explode and start the motor, that means gas must be in particulate form and mixed with the air. If it is cold then it condenses on the walls of the cylinders in a liquid form which is not immediately combustible. The choke increases the amount of gas in the gas:air ratio so that the bike can get the initial explosions going and warm itself up.
Finally, there is often a air/fuel mixture screw. These can be sealed off from the factory, and if they are they require no maintenance. They are there for minute adjustments to the mixture while the bike is at idle, and normally have no affect on the mixture while the bike is running at road-speeds. When a rider elects to add modifications to the intake or exhaust, it may be necessary to adjust this screw to reduce exhaust popping.
Speaking of modifications, whenever pod filters or freeflow exhausts are added, the carbs will likely need to be adjusted. Personally I think that pod filters are a bit superfluous for the the way that most people use them, unless you are also putting in racing cams and/or a turbo or whatever and really maxing out the bike, I don't think the advantages are there. However, it is possible to tune the carbs to accept pods, and you might get a little extra power.
These first videos are going to show how to clean carburetors.
After you clean your carbs you need to sync them. Here are two ways of doing that:
This is how to adjust carbs for mods to the intake and exhaust
If your carbs are leaking and overflowing, here is how to repair that
How to remove the carbs:
Here are two easy ways to re-install your carbs, on an inline 4 and a v-style motor:
Finally, don't forget to check your float heights!