I've looked into this extensively, and it's even part of why I went back to school for mathematics. I've looked a lot of the supposed brain training programs and so forth, which have not been proven effective. The things that I *know* work are - reading, learning mathematics, learning languages (has been shown to prevent alzheimers), and exercise.
Whenever I've seen a neuroscientist ask about the most effective "brain training" they invariably mention the last one. I hear a groan - I know there is every excuse in the book not to do it(no time, too tired, no discipline, bad knees, too hot outside, too cold outside), but there's no getting around it. People sitting around on their asses doing luminosity are wasting their time. To improve mentally you have *got* to have the physical end of it taken care of.
It's kind of a disappointing answer. We would like to just sort of sit there and do some sort of mental activity and "work out our brain," but that's only part of the picture. The brain is a physical thing. It needs oxygen and blood. Learn, read, do math, run (or something).
-Dave K