I was typing up a direct response to a friend when asked about learning different tactics, but it started getting so long that it made more sense to just post it on a forum for reference instead of in private. This is that post. Don't mind me.
Tetris:
If you just want to brush up your fundamentals on how to cleanly stack for Tetrises, check
this video by James Chen. Nothing too advanced, but he has some good pointers for planning a few steps ahead to avoid specific piece dependencies, which is important for avoiding holes and not cluttering up your well. If flawless, clean stacking isn't already second nature to you, then this is worth a watch.
T-Spins:
A T-spin Double sends the same amount of garbage as a Tetris, but it only requires half as many blocks to build, which means that it can be twice as effective at KOing the opponent if you're skilled at setting them up. It's kind of difficult to wrap your head around this at first, but
this video does a decent job at showing how to set up the hole + overhang to get it to work. If you *really* want to study T-Spin setups, you can check
this page on the Harddrop wiki. It's not really laid out in any kind of sequential order though, so it's just a matter of taking in as much as you care to. I think "Albatross," "TKI 3," and "DT Cannon" are some of the most popular specific setups based on what I've heard from a few other players.
If all that sounds a bit much, then don't worry too much about learning how to set up T-spins from scratch; just try to develop an eye on how to capitalize with T-spins while down-stacking through garbage. Sometimes you'll have garbage holes in the middle of your screen that aren't deep enough for a Tetris, and rather than just mindlessly clearing them out one line at a time, see if you can set up a simple overhang on top of some of them that allow for a T-spin. T-spin Doubles are usually the ideal thing to go for while down-stacking; Triples send more garbage but take a more concerted effort to set-up and leave your stack messier afterward.
Combos:
If you can clear multiple lines in a row with each piece that you get, then it counts as a combo. The longer a combo lasts, the more garbage is sent; combos that are 10 lines or greater cause a ton of damage. Combos stop once you lay a block that doesn't clear anything.
You can build a stack for the specific purpose of doing combos by up-stacking on 6 columns while leaving 4 columns intentionally blank. Just make sure to put 3/4ths of a block at the bottom of the 4-column well so that you have something to start the combo.
This post is kind of old but it goes through the basic strategy.
And when you actually sit down to practice combos, use
this chart to learn the best ways to keep extending a combo without breaking it. Ideally, you want to keep setting up the patterns at the top of that chart because those patterns have the most flexible options for extending the combo even further.
The biggest decision when setting up the combo is whether the 4-column well will be on the side or the center. A side 4w is easier to improvise while up-stacking, but if you stack too high then you may get KO'd early if the opponent sends you a bunch of garbage all at once. A center 4w keeps the top of the stack clear where the next piece spawns, so it carries less of a risk for an early top-out, but it can be more difficult to learn how to split your stack into two halves and still build cleanly.
Center 4w is clearly superior for normal Tetris vs. Tetris battles, provided that you're adept at building it. I highly recommend using rectangular JLO patterns on one side and jagged ITSZ patterns on the other, ideally with either an S or Z piece occupying the bottom of the well, such as in
the picture used here. While building the ITSZ pattern, try to save T or I blocks in the Hold queue for as long as you can, and dispose of S/Z blocks as soon as there's a valid place to put them. While building the JLO pattern, you must place the J and/or the L before you have a spot to place the O; if you have to place *both* the J and L pieces before the O, then stack them in such a way that the JL combination leaves an opening in the center of the stack so that you can slide in the O piece between them later. Because these patterns use 4 blocks on one side and 3 blocks on the other, you'll usually reach a point where the ITSZ side is considerably higher than the JLO side. As you approach the top of the screen, you'll sometimes have to break the patterns and start improvising.
I demonstrate most of this stuff in
this video, but I also intentionally cut the combo short in a few places to set up a chance for a Perfect Clear at the end.
(Note: Side 4w is considerably more viable in Swap mode. Because Swap mode has a garbage-blocking feature that lets you delay incoming garbage with each successive piece drop as long as you keep clearing lines, the risk of an early top-out is lessened. If you're building a side 4w in Swap mode and notice that you're about to be sent enough garbage to KO you, then start your combo and keep it going to neutralize the garbage before it actually hits your board. If you have a much easier time building a stack for side 4w than you do for center 4w, then it might be worth doing side 4w in Swap mode.)
Perfect Clear:
If you can clear literally every block on your Tetris board, then you send about 10 lines of garbage to the opponent. There are patterns you can learn to set them up at the start of a match with a decent chance of success.
Example video.
Puyo:
If you're completely fresh to learning Puyo patterns, start with
this post I typed up that has some basic tips for building a 5-chain stairs pattern without letting unwanted pieces ruin your plans. Beyond that, though,
this wiki actually does a pretty solid job at teaching various things to learn and in a mostly sensible order, so rather than type a whole lot more I'm just going to link it.
IMO, you should start by learning how to create 5-chains on an empty field with several different patterns: 3-1 stairs, 2-2 stairs, 2-1-1 sandwich, and 1-1-2 sandwich. Once you understand how each of them work, try mixing and matching them within the same chain so that you can become more efficient at using the pieces dealt to you instead of being forced to throw them away to the side. Once you can reliably build a 5-chain with any piece sequence dealt to you, you have to learn some kind of way to transition upward so that you can build a longer chain on the upper rows of the field. It's probably just best to read the wiki in sequential order for that.
If and when you're godlike enough to build a 10-chain reliably, then maybe you can start learning how to watch the opponent's field so that you can make tactical decisions on when it's a good idea to harass him with short chains that block off whatever he happens to be building. Sometimes it's more worthwhile to go for the quick kill like this instead of just building the longest chain you can manage. I'm sure as hell not good enough to make decisions like these in a real match yet, though. :V