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I use this function

getList[name_String] := Module[{options, idx}, options = Names[name <> "`*"];
   options = ToExpression /@ options;
   options = {#, Options[#]} & /@ options;
   idx = Range[Length[options]];
   options = {#[[1]], TableForm[#[[2]]]} & /@ options;
   options = Insert[options[[#]], #, 1] & /@ idx;
   options = Insert[options, {"#", "Option", "Options to this option"}, 1];
   Grid[options, Frame -> All, Alignment -> Left, FrameStyle -> 
    Directive[Thickness[.005], Gray]]];

To use:

 getList["NIntegrate"]

I modified the above a bit based on function I think I got from one of the Mathematica Guide books but I do not remember now which book it was. The methods can be seen under the third column there by looking for Method-> there. At least this is much easier than having to scan pages and pages of help looking for these things.

Replace the name of the command above to get other functions.