What is a foolproof way someone can commit suicide without owning a gun?
If you ask because you can't buy a gun legally in your state, go to Vermont. Guns are totally free there.
If you ask because you don't
want to use a gun, there are several ways. Very high doses of barbiturates or strong opiates like Vicodin would do, if you take 100 tablets or more. Take 10 at a time and wait at least 5 minutes, preferrably 10, between every intake. If you take it with small amounts of alcohol at each intake, death will be even more certain.
The exhausts from a car will do, if the car is standing in a garage and you put a hose from the exhaust pipe into the coupé. Cars without catalysts are the best for this method, though.
Throwing yourself infront of a train is a popular method in Sweden. It's even messier than shooting yourself, but it's almost 100% foolproof, especially if you're jumping from a bridge, so that the train has no chance to stop.