How to train tactics methodically

In sports, there are often times methodical ways to practice. In tennis, for example, you don't just play matches or just practice forehands, you practice hitting forehands cross-court deep into the corner target, then to the angled target, etc.

I'm wondering, what is the equivalent method of practicing tactics methodically in chess? Would it be to practice one motif repeatedly? Or is it to practice blitz+standard?

I'm wondering, what is the equivalent method of practicing tactics methodically in chess? Would it be to practice one motif repeatedly? Or is it to practice blitz+standard?

Neither.

In the chess world it seems to be to use some variation of "spaced repetition". There is a great answer by BlindKungFuMaster to a different question which says:

Spaced repetition is a learning technique that repeats content after increasing time spans according to learning success, i.e. faster for stuff you haven't grasped yet, longer if you do well.

In chess this is either used to learn a certain set of (easy) tactical exercises basically by heart ("woodpecker method" according to Axel Smith, Michael de la Maza, …), which is supposed to improve your tactical pattern recognition.

Since BlindKungFuMaster's excellent post Axel Smith and Hans Tikkanen have published a book expanding on the "woodpecker method" called "The Woodpecker Method" which includes some interesting history and background together with instructions and explanations of the method plus over 1100 graded exercise.

The main difference between spaced repetition and the woodpecker method is that Smith and Tikkanen emphasize increasing speed rather than time gap. Here are their instructions:

Step 1
Cycle 1: Solve as many exercises as you can manage in four weeks. These exercises are your set; and solving them brings you to the end of your first cycle. (The exact time period can be adjusted according to your lifestyle and circumstances, but try not to spend much more than four weeks. If you find yourself taking much longer than four weeks, you have probably either not been putting in sufficient time, or have included too many exercises in your set.)

Step 2
Take a break from chess for at least a clear day, and up to a week if you need it.

Step 3
Cycle 2: Solve the same set of exercises but faster: within two weeks is the target.

Step 4
Repeat steps 2 and 3, and repeat again. Aim to complete each cycle in half the number of days as the previous cycle (rounded up, when dealing with an odd number of days).

Step 5
The Woodpecker Method has been completed when the full set of exercises has been solved entirely in one day – or after the 7th cycle, if you are unable to solve the full set in a day. In the final two cycles, you should focus more on spotting ideas, patterns and motifs at speed, and less on the finer details of calculation.

Interesting to note that Axel Smith credits the woodpecker method (named after the translation of Tikkanen's name into English) with his achievement of the GM title. This is what he says early in the book:

As mentioned above, I trained with the Woodpecker Method in the spring of 2010. That summer, I achieved three GM norms and surpassed the 2500 barrier, all within a seven-week period. The positive eﬀects did not stop there: the following year, my live rating brieﬂy peaked at 2601.

Such quick results from any type of chess training are rare in my experience, but for me the Woodpecker Method seemed to be just what the doctor ordered! The increased tactical acuity and consistency that came from working so hard with the method significantly decreased my blunders and made me more confident at the board.

Would I have made the same improvement with some other type of training? It’s not impossible – but my playing strength had not taken any significant leap in years, so I had been at a loss as to what to do diﬀerently to succeed. Although the Woodpecker Method probably wasn’t the only way for me to raise my play, it certainly proved to be a way. The intersection of my interest in the human mind and my motivation to stop blundering surely helped me to devote more time and eﬀort than I would have put into my usual training.

What is the equivalent method of practicing tactics methodically in chess?
Would it be to practice one motif repeatedly? Or is it to practice blitz+standard?

Preface

Playing standard games goes along with tactics training, but clearly not a part of tactics training at all. Many masters use blitz games as part of tactics training; but whether you should use this practice depends on your experience.

A moderated amount of blitz, online or over the board, can help you keep sharp. Be aware, an overdose of blitz can literally destroy your chess thinking and turn you into a superficial player with very little chances of survival in longer time controls.

If you tend to play too fast in standard games (much less aware than usual) after playing blitz games, I recommend not playing blitz games at all (see the above quote as to why).

Tactics Training

Tactics training is not just one practice; it is rather comprised of a number closely related practices, each aiming one/more of the following:
(1) Get familiar with a theme (or a motif for that matter)
(2) Spot important themes in a given position

NB: I recommend doing them in the given order, that is Practice (1), followed by Practice (2) and finally Practice (3).

Practice (1)

Practice (1) is done especially when someone learns a theme for the first time. In (1), the player practices a large number of (relatively easy) puzzles of the same theme in one stretch. This can be done with tactics books where there are exercised arranged by theme, or with websites (such as lichess.org) that allow tactics training by theme.

The aim of practice (1) is recognition of a pattern (in simplest setting, at first). Here, the focus is on recognizing the pattern in a large number of puzzles in reasonable time (rather than doing a few hard ones). The hardness level of the set of puzzles can be gradually increased, as long as the player is still able to solve a large number of puzzles in reasonable time (the principle at play here is reward).

Practice (1) can be repeated spaced out a la spaced repetition method with or without targeting to reduce the time taken to solve the problem (the latter is the focus in the woodpecker method explained in Brian Tower's answer). Both spaced repetition and the woodpecker method seem to recommend using the same set of puzzles multiple times in order to learn the set of puzzles basically by heart. I personally recommend against it. I think using a very similar set of puzzles would be more beneficial (how similar works best is a topic worth researching). This is my recommendation because the aim is to get familiar with a particular pattern, not a particular position. At the least, one can make small changes in less relevant parts of the position (relevant relative to the pattern at hand). The downside of this is that you need someone to prepare similar sets of puzzles unless
(i) you are using a website that allow practicing puzzles by theme as well as rating level, or
(ii) you have a large set of puzzles along with hardness level and splitting it up into almost equal smaller sets is easy.

Practice (2)

Practice (2) is the most commonly available one. Some basically identify tactics training with practice (2). In (2), you are given a position where there are some tactical possibilities (opportunities or threats), and you have to find the best move. Quite often, (2) is a testing ground for familiarity with tactics and also the ability in calculation. Besides, practice (2) tests a player's ability to weight different factors based on their relative importance in the given position. Practice (2) is doable with a large number of chess books (exercises not by theme) and websites such as chess.com, lichess.org, chesstempo.com, etc.

In (2), more often than people realize, mixed tactics/themes is at play. For example, even in tactics training by theme (i.e., (1)), if two puzzles differ in hardness level, say puzzle 2 is harder than puzzle 1, then almost always puzzle 2 involves a larger number of other themes and/or themes at a higher level (different themes involved are usually missed since some themes are less appreciated than others; e.g.: gaining tempo, coercion, reloader, attack/remove the defender, opening/closing lines, trapping pieces).

Practice (3)

Many players find it easy to solve puzzles, but unable to spot easier ones in their games (see this question for instance). Practice (3) addresses this issue. Here, a set of positions are given, and the question is "What is your move in this position?". A position in the set may or may not involve a tactic, and it may have more than one answers (e.g. depending the plan the player comes up with). This simulates the game situation more closely.

A set of positions with this idea can be found here.

Also, a set will be timed and the player is asked to solve the maximum number of puzzles within the specified time (time should not be too low). Here, not only calculation, but also judgement is tested. The player has to decide which positions require a more thorough calculation. There is no guarantee that there is tactical resource for you (e.g. no automatic sacrifices). Deciding when to calculate deeply is a crucial skill for a serious chess player.

Although there are websites that attempt to do practice (3), their success in doing so is questionable (they succeed better when the number of themes involved in the set is larger and also involve positional themes in addition to tactical themes). It seems to me that puzzles in chesstempo.com have this nature more compared to those in chess.com and lichess (note that choosing tactical positions from games does not simulate game situation). I think a coach can do the job of preparing a set of positions for practice (3) much better (for this practice, only themes the player is closely familiar with should come up in the given position).