The best thing about tactics training is that if you do it, even perhaps badly, you will get better at chess. For the most part my discussions will assume that you have learned the basic elements of tactics. Tactics are nothing in themselves, but must be measured against the object of the game, which is to deliver checkmate. So, it's understandable that the most popular tactics drills are those that end in checkmate. (Tactics may also end in a material advantage or simply in an improved position.) If you haven't learned how to deliver basic checkmates, find one of the many free sites that will help you learn mates such as K + Q vs. K, or K + R v. K, etc. You must also be familiar with simple endgame theory. You won't recognize some winning tactics if you don't recognize simple winning endgames. If you don't have a basic endgame understanding, I strongly recommend that you read at least the first Two Parts of Silman's Complete Endgame Course, and I would suggest that you go further by reading one Part beyond your present rating (the book is divided into Parts based upon the reader's rating). I also assume that you have an understanding of tactics elements such as skewers, pins, forks, double attacks, discovered checks and the like. If you don't, read Bobby Fischer Teaches Chess. Beyond the above, the recommendations here make no assumptions about a player's abilities, but rather presumes that each player will design a tactics drill set that fits his or her skill level.
There are three things I have in mind when studying tactics. First and foremost is pattern recognition, which can be described as the aspects of chess problems that repeat themselves. In general, the more patterns you command firmly, the more likely and quickly one or more will emerge in your thinking during a game. Second, the solving of tactics problems provides a good platform for improving visualization skills, which might be described as how accurately you see the board during and after some sequences of moves. And third, tactics provides a good platform for improving your calculations, which begins with candidate move selection, and continues with branching, pruning, and evaluating skills. None of these things, however, have any meaning until you understand how to win a chess game and the basic elements of tactics. You have to begin with an understanding of what's to be recognized, visualized, or calculated. Once you have the requisite skills--I'm guessing as measured by, or near, a four-digit Elo rating--then you're ready to start the "next" level of tactics training.
At this point, go ahead and read de la Maza's Rapid Chess Improvement. It can be read in an hour or two (or read the summaries of his program in two parts at ChessCafe). You should read the book with an accepting mind restrained by a liberal dose of skepticism. Reasons for accepting the book abound in de la Maza's text; Jeremy Silman will help with the skepticism. Then, unless you need someone to rigidly prescribe your learning steps for you, develop your own plan and goals for drilling tactics. A good place to start is with CT-ART 3.0 (ART). ART is a moderately-priced, cleverly developed software package of about 1200 problems. The problems range from the simple (one-move shots) up to the substantially complex (tactics that might be missed by a titled player in an OTB game). You can divide the problems in various ways, including by degree of difficulty. The simplest problems are identified by a "10," the next by a "20," and so on. One way to begin, for example, is to establish for yourself a subset of the 1200 problems, say the 10, 20, and 30 level problems and drill those until you recognize the boards and solutions instantly. As you go through these problems, you'll be visualizing and calculating the solutions at the outset (as you would do in a game), but as you get familiar with the positions, you'll begin instantly recognizing the patterns on the board. (Sounds a little like Rapid Chess Improvement, ey? A little, but adapt the parts that seem right to you to your own plan. It isn't necessary to devote all of your time to tactics, nor is it necesary that you have hours for study each day. And, finally, the problem set that you create for your drilling should be changing and getting more difficult with time.) As you do more and more problems, both in ART and elsewhere, you'll discover that many of the patterns are transferable to other problems (and presumably to your game positions). You will get better. Consider also using a tactics trainer, like the one at Chess.com, to measure your progress (in addition to watching your rating). The more patterns you recognize, ultimately measured in the thousands, the better your chess skills. Please note that selecting the set of problems you will ultimately keep in your drill set should be a large part of the training. The calculations and visualization you do in identifying problems that are too difficult for you at the moment is part of the improvement process. Today's problems that are too difficult won't be tomorrow. Similarly, you're going to discard problems that you solve in, say, under 10 seconds. You've already absorbed that particular problem into your chess thinking.
Don't use only ART, but also select some good solid basic (but not too easy or too hard) problems books and other sources of problems. You want problems that are yeilding discernible patterns that you can learn and build upon. If you use Chessbase, you can build a database of these problems, with each problem as a separate "game" in the database. This requires some upfront work, but makes the problems easier to drill in the future. As you progress, you'll add patterns (problems) to your chess thinking, and the learned patterns will increase in both number and complexity. When a problem is learned entirely beyond any reasonable doubt, discard it from your set and replace it at the upper end of your set with a difficult problem. When the sources I've mentioned here, or your own, have become too easy, look for more advanced problems books to provide new material. The ChessCafe puzzle books come to mind. I won't pretend to know all of the possible sources of tactics problems, but other good sources at about the 10-40 level in ART are Dan Heisman's Back to Basics: Tactics and Jeff Coakley's Winning Chess Exercises for Kids, which is not so simple as it sounds. (Please note that I have no affiliation with any commercial chess interest whatsoever. I recommend what I've tried.)
Now develop a problem set for your ability, ranging from the easy to the difficult. (If you can't solve the problem the first time in 10 minutes of visualization/calculation, you're not ready to move it into your problem set.) The "set" should consist of ultimately 1000-2000 problems. Learn the set cold, and then add and take away from it with time. My sense is that after a year or so, you should have discarded between a quarter to a half of the easier problems and added an equal number of more difficult problems. If you're working long and often, it's possible that you could turn the set over entirely, even more than once, in a year's time. Building and maintaining the set is part of the suggested training. I leave open the distinct possibility that you'll have a better idea, and I hope you'll share it in the comments here.
2D vs. 3D. Does it matter if you're looking at a two-dimensional computer screen or a three-dimensional chessboard? If you're just beginning, or you don't like the 2D screen or page, use a board. With time, and you'll know when it arrives, there'll be no appreciable difference between visualizing on a live chessboard versus a computer screen or page. My suspicion is that this ultimate non-difference relates to the way you think about the game, and specifically, the way you visualize the play.
A final word. Your training sessions should range in my view from 15 minutes (short) to two hours (long). You should aim for at least two long sessions a month. Do not quit on the problems when you're first attempting them. And you know that some will come easy with instant recognition, and others will be unsolvable after 10 or even 20 minutes. On the latter, make your best first-move selection and then reason through the entire calculation to a conclusion. DO NOT touch the board or the mouse (move the pieces only in your head), and DO NOT take a stab at a first move out of frustration and then test it by the solution. (This is especially tempting in ART--don't do it.) If the problem genuinely leaves you stumped after 15 minutes or so, move on to another problem and come back to it on another day. And note that this is not a problem that you should have in your drill set, at least not yet. Please don't misunderstand. It's perfectly okay to get the problem wrong--it's not okay to take a stab at a move before reasoning it out to your best conclusion. More later.
[Note: CT-ART 4.0 is now available from Convekta. Convekta claims that the basic problem set has been increased by about 1,000 problems.]