Your mower's carburetor has a stuck float or some type of debris (rust, fuel varnish, etc) holding the float valve (sometimes called the needle) off it's seat. As, by your own admission, you are not a mechanical type person, have a trusted mechanic clean & repair your carburetor as required.
The worst case situation would require a replacement carburetor. However, if it's cost effective, a good mechanic can clean & repair a carburetor. Therefore, never trust anyone who is quick to say, without even investigating the problem "carburetors can't be cleaned" or "it's cheaper to replace them," then wants to sell you a replacement carburetor for $50 to $100, plus a couple hours of labor.
In the meantime, check your mower for a fuel shutoff valve in the fuel line between the fuel tank & carburetor. If your machine has one, close it to stop the fuel leakage.
Also, when the engine is not running, the fuel valve should always be closed on all machines that use gravity feed fuel systems. I don't care what anyone else says on this matter. It's a safety issue, as the slightest debris or cocking of the float valve will result in a shed, garage or utility room floor full of explosive gasoline.
