The specific study cited was an analysis of the Seattle Longitudinal Study of Adult Intelligence. It's followed over 5,000 people for more than forty years. A summary can be found in Essential Papers on the Psychology of Aging. Our citation is from this page.

This 2006 article discusses cognitive training benefits in general: "Participants who had the training showed immediate improvements in memory, reasoning, and speed of processing. When the participants were tested five years later, the improvements had been sustained." An earlier report covered the specific training:

Those in the memory-training group were taught strategies for remembering word lists and sequences of items, text material, and main ideas and details of stories. Participants in the reasoning group were taught how to solve problems that follow patterns. Such strategies can be used in tasks such as reading a bus schedule or filling out an order sheet. Speed of processing training focused on the ability to identify and locate visual information quickly for use in tasks such as looking up a phone number, finding information on medicine bottles, and responding appropriately to traffic signs.

There are many commercial "brain fitness" tools available, from books to online programs to videogames. Some researchers believe that these only teach the user to do one thing well, and don't enhance overall mental fitness.