What are all the different ways Riot punishes players?

There are also ID bans, which are where Riot will automatically perma any account they discover being used by certain people, regardless of whether or not there was any behavior on that account. Tyler1 is an example of someone who was on an ID ban.

I don't think there's any place in particular to find all of the different punishments that Riot employs. You can certainly check out Riot Support, though the information there may not be precisely what you're after due to FAQ formatting.

That said, there are quite a lot of different punishments (some of which are largely the same) that Riot uses, so these are the ones that I can recall;

Chat Misbehavior

• 10-game Chat Restriction - Typical first punishment for moderate/light offences, simply ten games where your allotted chat is restricted to teach you to use your chat well, and that, if you don't have anything nice/constructive to say, it's altogether better not to waste time saying it at all.
• 25-game Chat Restriction - To quote Jimmy from Ed, Edd, & Eddy, "Second verse, same as the first". Same restricted chat, just 15 games more as a harsher punishment for continued misbehavior.
• 14-day Suspension - After the 25-game Chat Restriction, continued misbehavior will result in much stricter punishment, and a warning that continuing to break the rules will result in a permanent account suspension.
• Permanent Suspension - Assuming someone ignores the first time the ban-hammer is dropped, Riot treats players who belligerently refuse to follow the rules with a permaban, serving as a message; "If you can't be bothered to play by the rules, we can't be bothered to have you playing at all."

Zero-Tolerance Chat Misbehavior

• 14-day Suspension - For egregious chat misbehavior that falls under zero-tolerance (such as hate speech or encouragements of self-harm), Riot immediately skips the first two chat punishment tiers, because players are expected to know that such behavior is completely inappropriate and unwelcome in League.
• Permanent Suspension - Following the 14-day Suspension, any chat misbehavior will result in a permaban. However, there have been rare cases of players jumping straight to the permanent ban as well; though this is only for the worst types of offences.

Gameplay Misbehavior

• 14-day Suspension - Since trolling and intentional feeding have nothing to do with the chat, chat restrictions can be skipped and Gameplay Misbehavior is met with a 14-day suspension on the first verified offence.
• Permanent Suspension - Continuing to troll or intentionally feed after the 14-day suspension will result in a permanent ban.

Offensive/Inappropriate Screenname

• Forced Name Change - Riot's rules extend to screennames and Club names as much as it does to chat, and the typical first punishment for breaking the rules through screennames is a forced name change.
• 14-day Suspension - In the event that a player decides to act clever and change their screenname from one offensive thing to another, whether to spite Riot or because they disregard the rules in general, the next time they're reported for it, they'll be given a 14-day suspension. I'm not sure if it comes with another forced name change, but I'd imagine it would.
• Permanent Ban - As with other instances of players going out of their way to flout the rules, players who consistently change their screenname to something offensive or inappropriate despite warnings and punishments will be given a permanent ban on the third and final offence.

Cheating

• 14-day Suspension + Ranked Ineligibility - In the event of a player being found having their account played on and boosted by another player, both parties (assuming a clean slate) will receive a 14-day suspension and both will be locked out of eligibility for End of Season Rewards, as an apt punishment for illegitimate play.
• Permanent Suspension - The follow-up punishment for any account punished a second time for boosting (whether the booster or the boostee), as well as the first and only punishment for other verified cheating offences, such as botting, scripting, etc.

Honor Drop

• Honor Progress Penalty - For Chat-related offences that are not quite enough to merit a mainline punishment (like a Chat Restriction) but still verified to be rulebreaks, Honor Progress for that match is slowed/halted, which can cause Honor progression to take far, far longer than normal if behavior adds up.
• Drop to Honor Level 1 - For the first 10-game Chat Restriction, players are also issued an Honor penalty taking them down to Honor Level 1, along with the associated ineligibility for Ranked Rewards/Clash until they reclimb to Honor Level 2.
• Drop to Honor Level 0 - For repeated offences or severe first-time offences, such as boosting or zero-tolerance chat, the punishment is followed with a drop to Dishonorable Status; no ambient key fragment generation, and ineligibility for End of Season Rewards or Clash participation.

This all is pretty much what I've learned through reading the Player Behavior boards; between players themselves bringing their cases forward to seeing Rioter comments on penalties and relevant issues. I may well have missed something, but my recollection is by no means exhaustive or perfect.

Hopefully you find this information useful. If you have any further questions, feel free to ask.

You mean the way riot minorly inconveniences players by forcing them to make a new account, accomplishing absolutely nothing from a disciplinary standpoint?

Aside from those others have already mentioned;

I've seen 30 day bans for win trading in S8.

There's leaver buster for 5/10/20 minute x 5 games

Dodge penalty for 6/30 minutes

and our favorite conspiracy punishment on how you'll always get inters, griefers and feeders in your promo games.

In addition to what was already said, there are low priority que penalties for leaving games or AFKing.

You get a wait time of either 5, 10, or 20 minutes before you can actually enter the que for a game. You get those 5 games at a time, and unlike other punishments they do not affect your honor level.

sometimes like me you get ip banned that sucks, but normally just chat restricts and 14 days ban or just straight up perma bans

Aside from the stated punishments?

Does anyone believe there are other ways that they punish players and do not inform us about these actions?

14-day Suspension - Since trolling and intentional feeding have nothing to do with the chat, chat restrictions can be skipped and Gameplay Misbehavior is met with a 14-day suspension on the first verified offence. Permanent Suspension - Continuing to troll or intentionally feed after the 14-day suspension will result in a permanent ban.

I haven't had such a good laugh in YEARS. These are non-existent.

10 game chat restriction 25 game chat restriction 7 day ban 14 day ban perma ban While these tiers may exist its possible you may skip some entirely, heres an example; you tell your 0/36 jarvan to "kys" you will instantly get a 14 day ban.