There currently are no good general solutions, so the best tool(s) to use strongly depends on the specific problem you're trying to solve, resources you have available, and how good the answer needs to be.
Reading through the Russell & Norvig book would give you a good overview of the sorts of techniques available.
Unfortunately, too often, that perspective is lost. I know of no general solution to what defines intelligence. So I'm very dubious as to whether an encompassing artificial version is possible.
I see lots of specific solutions to specific problems. That, to me, is the best approximation of intelligence. To the extent that many specific solutions can be approximated and optimized, we'll be very well off. It's easy to denigrate a calculator and spell-checker, but I seem much more intelligent than I would be without them.
It's not like people haven't been trying. Indeed, the great aspiration to understand humans is the effort to define our understanding (how's that for a circular argument?).
Moreover, you prove your own point - the one I was agreeing with initially out of everything said in this thread. A rocket ship or heart transplant are specific solutions to specific problems. The analogy to intelligence would be one universal solution to flight or one universal solution to getting oxygen and glucose into cells. It's not that a solution isn't possible. It's just that the hope for THE solution is misguided (see also THE cure for cancer).
I really like the flight analogy because of the length of time people put into finding THE solution.
But what we end up with instead are rockets, and prop planes, and jet engines, and airfoils, and gliders, and helicopters, and hoverboards...
Reading through the Russell & Norvig book would give you a good overview of the sorts of techniques available.