How do I get my bike to run after storage?

    Most common problem for a no start after sitting for a month or more is stale fuel. The fuel in the gas tank may be fine, there is usually enough volume of fuel in the gas tank to keep it from spoiling right away. But the fuel the engine runs with is in the bowl of the carburetor, and the fuel bowl only holds a very small amount.   The bowl is also vented, so the fuel loses good vapors
even faster.  

    So the trick to getting your bike running is to get some fuel into the carburetor bowl that will still burn.  To do this you need to drain the stale fuel out.   Most carburetor bowls have a drain screw at the very bottom.

kymco Yup carburetor    

The carburetor on this Kymco model is very similar to many other mopeds. There is a rubber curtain around the carburetor bowl, but you can see the drain screw sticking out.    Some bowls have a bolt going straight up in the center that is removed to drain, but most are of this style.  Loosen the screw a few turns and you should see fuel dripping out of the screw or a drain hose.   After about 1/4 cup comes out, retighten the screw.  You may need to crank the engine over a few seconds to get fresh fuel to flow from the fuel tank and refill the carburetor before it will start.  Most mopeds have automatic fuel shutoff valves,  that is why it needs to crank a bit to refill the carb bowl.    
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