I just basically run through them. Or if you suddenly notice you lose many games by a certain thing, either do tactics on that or just try to think more in those types of situations!
Tactics Training - Puzzles

Like ricemaster says, just run through them. One after another. Spend some time (10, 20 or 30 minutes per day, whatever you can afford) just trying to complete them. After a while you'll start to notice patterns and find the solutions. Then the puzzles will get more difficult and this process will repeat. Sometimes you'll go down in puzzle rating and sometimes you'll go up. When you're getting the learning process right you'll see the difference in the games you play.
I use two approaches. 1) Easier puzzles based on theme. 2) Harder random puzzles. I think the first develops pattern recognition and intuition, the second develops calculation and visualisation. The chess. com themes can be a bit confusing. The classification isnt always reliable. For example you might do 'Pin' puzzles and there will be a pin in the position but it's not playing a significant role in the solution. I gave up on the chess.com themes and use other sites. The random puzzles on here are useful though.
Do you think working through puzzle books is better than the online puzzles here and elsewhere? Or vice versa, i.e. are online puzzles more efficient?
I'm not sure where the chess.com puzzles come from, but for example I'm doing the On The Attack series on Chessable and all the puzzles there come from games between players rated over 2200 (or something like that) so the tactics have all appeared in real games between strong players. The author explains this in the introduction. I really dont know if it is something that is important though.
Just to add that some tactics are very thematic. For example there are a whole range of Bxf7 combinations in the Italian Game that someone playing that opening should drill.

What I've heard recommended by various titled players involved in chess education (including IM Danny Rensch of Chess.com) the ideal way to use tactics puzzles on the site to study is to choose Custom and study one or a handful of themes at a time. For example, I'll spend some time practicing only puzzles marked as Fork, Pin, or Skewer. By limiting the puzzle themes to principles you've spent some time learning about, your practice becomes more about starting to learn the relevant patterns rather than trying to scour the board looking for the best of all possible moves. Not that that isn't good practice too, but if you're having trouble seeing mate in 3, you probably don't want to be doing puzzles about finding the hanging piece.
What I've heard recommended by various titled players involved in chess education (including IM Danny Rensch of Chess.com) the ideal way to use tactics puzzles on the site to study is to choose Custom and study one or a handful of themes at a time. For example, I'll spend some time practicing only puzzles marked as Fork, Pin, or Skewer. By limiting the puzzle themes to principles you've spent some time learning about, your practice becomes more about starting to learn the relevant patterns rather than trying to scour the board looking for the best of all possible moves. Not that that isn't good practice too, but if you're having trouble seeing mate in 3, you probably don't want to be doing puzzles about finding the hanging piece.
I've heard from some coaches that they do not recommend online puzzles but instead books. I wonder if this is why... maybe because the books may be organized into themes? Seems like choosing custom and themes may be the best way for me to do tactics training online. Thank you!

I've heard from some coaches that they do not recommend online puzzles but instead books. I wonder if this is why... maybe because the books may be organized into themes?
I'm a regular listener to the Perpetual Chess Podcast, which is a great source of interviews of chess educators, people trying seriously to improve at chess as adults, and figures from the professional chess world. This topic has come up a number of times, and the reasoning is always the same: What you should seek to do with puzzles that require more than one move to solve is to visualize ahead and plan all the moves before attempting one of them. This is much easier to do with a book. On chess.com, it's very easy to make a guess as to move one and then just try things from there, seeing what the computer does in response.
IM Andras Toth goes as far as recommending that one answer puzzles by writing down, on a piece of paper, all of both sides' moves. He's pretty negative about puzzle practice online.
I personally have been attempting to visualize all the moves in puzzles on Chess.com before making the first one, but of course I sometimes get credit on the site for answers where I didn't correctly anticipate the computer's response and yet was able to see what to do next after seeing it.

cardio: puzzle rush 3/5 minute & puzzle battle (go fast & try to anticipate).
building intuitive pattern recognition, speed & reflexes in faster time controls.
strength: survival rush & standard puzzles (go slow & try for 100% accuracy).
improving your exact calculation, evaluation & move-selection in slower games.

Do you think working through puzzle books is better than the online puzzles here and elsewhere? Or vice versa, i.e. are online puzzles more efficient?
I've often questioned this myself, I've heard that the puzzles in books are "higher quality" whatever that means. I think one advantage books have over online puzzles, is that other then being portable (not a big deal with today's technology) you can go back to a puzzle with ease, online you can't really do that, especially if the puzzles are randomized, I'm not saying it's not possible, just a hassle, tagging the problem and the like.

you can go back to a puzzle with ease, online you can't really do that, especially if the puzzles are randomized, I'm not saying it's not possible, just a hassle, tagging the problem and the like.
At least if you are doing puzzles on chess.com, you can visit your puzzle history by clicking on this button on the main puzzles page:

you can go back to a puzzle with ease, online you can't really do that, especially if the puzzles are randomized, I'm not saying it's not possible, just a hassle, tagging the problem and the like.
At least if you are doing puzzles on chess.com, you can visit your puzzle history by clicking on this button on the main puzzles page:
I rather have the puzzles in a book but that's me personally, I think there are pros and cons to both.
What is the proper way to work on Tactics using the Puzzles here on Chess.com? Custom, All Themes? Or do you pick a particular theme and work through that?
Or is there a better way to practice tactics?