As brain training is still new as of this writing, and evidence of it even more novel, I will not devote myself here to games such as Brain Age with no evidence backing them up, but will strictly stick to implementations of the concept that have evidence in their favor, even if preliminary.
N-back is the first implementation of the brain training concept that was demonstrated to work on a statistically significant level. It consists of flashing stimuli to a person, both in serial and in parallel, and the object is to tell it whether a given stimulus is the same as the corresponding stimulus N turns ago. For example, in 1-back, you might get the following sequence of letters:
A B C C B A B A A
Since N = 1 in this case, you'd be looking for letters repeated twice in a row. The correct answer, in this case, is to buzz in on the fourth and ninth letters, since they are repeats of the letter before. But now, let's switch to 2-back. Here, you're looking for repeats of two letters ago. In the above example, you'd buzz in on the seventh and eighth stimuli. In 3-back, you'd buzz in on the fifth stimulus.
But, you don't have to work with just one stimulus. Indeed, almost nobody trains with regular N-back anymore, but with a variation called Dual N-back (DNB). This variation uses two stimuli, not one. So, for example, you might use the above sequence of letters, but also give each a different colour, or you might play a sound at the same time. You would then have to remember both stimuli, and tell whether each one was the same as the previous. Take the following sequence:
A B C C B A B A A
Let's say we're playing D1B; then you'd buzz in for colour at stimulus two and for letter at four and nine. If we were playing D2B, then you'd buzz in for colour at stimulus four, for letter at stimulus eight, and for both at stimulus seven. There's no limit to the number of stimuli, either. For three stimuli, it would be called Tri N-back, for four it would be Quad N-back, etc. The number of things to remember goes up with both the number of stimuli and the number N, according to the formula M(N, s) = N(s + 1), where M is the number of stimuli you must memorize, N is the number of turns back that the comparison is made, and s is the number of stimuli given each turn. This means that your working memory must be able to process a large number of stimuli simultaneously in order to succeed at higher levels (more on that later).
The most popular implementation of N-back is this open-source version from Brain Workshop. It allows you to manipulate both N and s, and adapts to your skill level.
Posit Science is a corporation that manufactures brain training software. They have three packages of software: InSight, DriveSharp, and Brain Training. The former two deal with visual processing (with InSight essentially being a strict superset of DriveSharp), whilst the latter deals with auditory processing. Since the vast majority of the information we receive each day is visual or auditory, this training is significant, and is very close to directly challenging your working memory. Because of this, InSight and Brain Training complement each other nicely, and Posit Science offers a Total Training Package that contains both. Besides N-back, Posit Science is one of the only training methods that's been demonstrated to work. Unlike some implementations of N-back, though, the software from Posit Science is rather expensive.
Brain Training tends to focus on the phonetic aspects of the auditory information we receive. The first exercise, "High or Low?" gives the person two sweeps, which can either go from low to high or high to low; the point is to correctly answer which ones they were. This represents the similar sweeps in ordinary speech, and the sweeps start at 40 ms, 1000 Hz sweeps, spaced 600 ms apart; however, this gets harder over time. "Tell us Apart" gives the player a phoneme (a single syllable), and the player must select the correct one from two similar ones (for example, doe/toe, bu/do, and sah/stah). The first few levels are artificially emphasized, but the emphasis continuously decreases, until it reaches the level of ordinary speech. "Match it!" and "Sound Replay" build on the first two, and asks the player to remember sequences of phonemes; in the former, it's done in a format similar to the popular game, "Concentration," and in the latter, the player is given a sequence of such phonemes, and the person must give the correct order. "Listen and Do" builds even further, and has the player remember specific commands. Finally, "Story Teller" is the culmination of the other five exercises; the player is told a section from a story, and must remember specific details about the story. Each training session consists of four of these exercises, at fifteen minutes per exercise. Also, to stimulate the brain's learning centers, the player is rewarded with a soothing or humorous picture or animation after getting a certain number of correct answers.
InSight is different, and not just in its focus on visual processing. For one thing, it only has five exercises. These exercises are Bird Safari, which flashes several birds on screen, one of which is different from the others; Jewel Diver, which asks to keep track of several moving objects; Master Gardner, which flashes several plants on screen, and the player is asked to click on the ones that match (it can either be two out of three, or three out of five); Road Tour, which flashes a certain type of car in the middle of the screen as well as a road sign somewhere on the periphery; and Sweep Seeker, which is similar to "High or Low?" except with visual sweeps. The exercises are designed to improve, to varying degrees, the brain's useful field of view, processing speed, and divided attention. This software sets goals for the player, and measures achievement via periodic assessments.
Advanced Attention developed this particular piece of software, called CogMed, to improve the attention span of children with ADHD or similar disorders. Like N-back and Posit Science, this software has been demonstrated to work, though it hasn't been tested on anyone with normal attention span, to see if theirs increases as well. At up to $2400, however, it's even more pricey than Posit Science, and is thus out of the price range of most people who would benefit from this.
~~Working Memory Workout~~
However, the problem here is parallel to that of transhumanism. Most brain training software is rather expensive. Like transhumanism, however, the solution is the same: allow an open-source community to develop, and create such software for themselves, which anyone can easily download, use, and modify at will. Most implementations of N-back, as mentioned, already do this. Another great example is Working Memory Workout. Available both as a collection of flash applets in a series of blog posts and as a free download (although I'm having trouble getting this to compile, and the creator of the software hasn't yet responded to my emails), this is probably the most popular open source brain training game in existence, besides N-back (not to mention, N-back is among the games in the WMW software). As the name suggests, the games are designed to improve working memory, and—at least in the case of N-back—definitely work, as well.
~~Intuition vs. Strategy~~
When I was first playing DNB, I noticed that if I was thinking hard, but not trying hard to remember the sequence of events, I could still get the correct answers, even though I wasn't focused on remembering. As it turns out, I'm not the only one who noticed this; plenty of other N-backers use this strategy. The idea is simple: we're not trying to get better at rehearsing sequences of events in a short space of time; rather, we're trying to develop a new type of mental process, which makes use of our non-conscious processing abilities. On the face of it, it has a lot going for it; after all, non-conscious processing, though inaccessible to us directly, is more potent than conscious processing. Neuroscientist grad student has drawn the following analogy: "Even though you have this supercomputer in the room, we're only allowed to use our TI-83 calculators. The supercomputer is password-protected, in a language we don't even understand."
So, is the "intuitive method" as it's called, where you think very hard and wait until it "feels right" to buzz in, effective? Well, you can find some people (check the N-back FAQ link above) who express dissatisfaction with it, and even more people who simply find it "hard to believe" (seriously, I'm not kidding), but I still think the evidence is more in its favour. Remember the Posit Science software, which has been demonstrated to work and has a board of top neuroscientists? That software strongly advises that you "trust your gut" when doing its exercises. It also seems that this might explain the popular advice to "go with your first inclination." In both N-back and Posit Science, I've rationalized away a gut feeling I'd had, to my detriment. Finally, it seems that developing a non-conscious process is more desirable than developing a conscious process. Not only is non-conscious processing more powerful, but it operates without needing to consciously focus on it. Both of those are plusses over the alternative. So, if you want my (admittedly unqualified) advice, use the intuitive strategy, and strive to develop this new, non-conscious mental process, and to make your non-conscious processing in general more efficient.
~~Working Memory and Fluid Intelligence~~
So, why does cognitive training work in the first place? In principle, what they're supposed to do is increase a person's fluid intelligence, or to solve problems logically independent of acquired knowledge. This is distinct from crystallized intelligence, which is dependent on acquired knowledge. For example, a physicist who knows that Maxwell's equations describe the classic electromagnetic force has crystallized intelligence, but a physicist who can come up with new equations for certain conditions, with reasoning alone, has fluid intelligence. Fluid intelligence is suspected to be related to what we generally understand as "intelligence." So, how is fluid intelligence improved? By increasing what is known as working memory (or the ability of the brain to memorize arrays of information, and to recall them while they're not actively being thought of); or, in the case of CogMed, by increasing attention span. Both of these processes are known to be a part of fluid intelligence, so increasing them should increase fluid intelligence, at least in principle.
How N-back increases working memory is obvious; it pushes your brain to process larger arrays simultaneously. Posit Science is somewhat more roundabout, but ultimately, all the processes I mentioned—useful field of view, language analysis, divided attention, etc—involve analyzing and synthesizing larger arrays of information. CogMed, meanwhile, focuses on attention span rather than working memory. Actually, Torkel Klingberg has argued in the recent Entertainment Software and Cognitive Neurotherapeutics Conference that working memory and attention are operated by the same neural hardware, so they can be thought of as one, singular process. That does make some intuitive sense, since the ability to focus one's attention on an array of information does seem somewhat analogous to the ability to retain this information. This is definitely worth considering further study.
~~Learning and Rewarding~~
In the Brain Workshop implementation of N-back, you can set a Boolean variable called SHOW_FEEDBACK to either True or False, which either enables or disables the feedback mechanism of it. If this variable is enabled, and you get a certain trial right, the text below flashes green; otherwise, it flashes red. It is mostly a matter of preference which one you do; on the one hand, it could stimulate your brain's reward mechanisms, thus helping it learn; on the other, some have reported it as distracting. Personally, I always keep it on; it helps me know where exactly I went wrong (sometimes I even realize what my mistake was), and I also find the green flashing aesthetically pleasing, so it actually feels good to get answers right. The game even seems rather fun doing it with feedback!
Brain Training, from Posit Science, has a somewhat more sophisticated feedback system; it allows you to choose a theme before every session, such as Animals, Family, Music, and Colors. Every time you get a trial correct, it builds a picture, which is completed after getting a certain number correct. After increasing your level, it rewards you further with an animation. The pictures and animation can either be humorous, as with Family and Music, or soothing, as with Animals and Colors.