Troubleshooting 101:General engine troubleshooting
When a bike suddenly stops working, there are three "systems" to check. Note that this does not apply to a bike which gradually stops working (then, think valves or carb cleaning). This is a pretty basic guide, but hopefully it will be helpful to anyone who's having trouble with their engine. If you can run through this and narrow down your problem board members will be much more likely and able to help you diagnose the exact trouble.
Fuel is what gets consumed to make the fire that makes the engine turn. Fuel is stored in the tank, travels through the petcock (which has two potential blockers, in the petcock lever and the vacuum diaphragm, not to mention crud getting caught inside it somehow) and fuel lines into the carburetors, where it's atomized and sprayed into the cylinders.
Things to check on the fuel system:
Air arrives at the engine by way of the airbox, air filter, and carburetors. Air has to be mixed with the fuel in the right ratio to burn well. Too much or too little air and the fuel won't burn right. There's not a lot that can go wrong here, but pull off your seat and check to make sure there's nothing covering those two intake holes just behind the fuel tank. If that looks clear, check the air filter to see if it's disgustingly dirty (if it's just a bit dirty, that's not the problem). You could check for further problems like leaves or mouse nests stuck in the intake, but that's quite unlikely if the filter's properly in place.
Spark makes the fuel burn in the presence of air. Obviously, without spark there will be no fire. The spark system (in very basic terms) is composed of the battery, the ignition module, the coils, the wires connecting them all, and the sparkplugs. The battery supplies power to the ignition module and the coils. The ignition module tells the coils when to fire. When the coils fire, they send a jolt of high-voltage electricity down the sparkplug wires to the sparkplugs. The sparkplugs are nothing more than carefully adjusted wires which have a precise amount of space between them. The sparkplugs only work when they're touching the engine case, since that's how they complete the circuit.
Things to check on the spark system:
If nothing in this guide helps, then you're either doing something wrong or your bike has been gradually getting worse and you didn't notice it. Gradual problems are likely to be the valves going out of adjustment, or varnish slowly building up in your carbs if you don't ride very often. There's no easy way to check if it's the valves, but symptoms include running poorly at low speed or idle, ragged or variable idle, and hard starting.
Side note: reading spark plugs. Since spark plugs are the only part of the combustion chamber you can readily remove from the engine, you can use them to see how the engine's doing. Spark plugs should be a lightish tan color if all is working correctly. If a spark plug is really heavy black, the engine's running rich. If it's white, the engine's running lean. If it's lightly black, that still suggests a rich mixture, but maybe not enough to freak out about. Compare yours to the ones in the sparkplug guides.