What rules does Tenhou use?
Japanese rules, also known as "riichi mahjong". It doesn't use toudai rules (Tokyo University) strictly, though. See Specific Rules for information on Tenhou's quirks.

How do I play Japanese mahjong?
Refer to the list of resources for information on how to play. This is not a full list, but it lists the best resources.

Where can I find information on scoring and a list of yaku?
Without a doubt, Wei-Hwa Huang's Japanese Mahjong Scoring page. This covers absolutely everything, including both English and Japanese terms. Avoid linking anything else, as most other resources are just diluted versions of the content of this page.

Can I cheat?
It is impossible to predict what tiles will be drawn, or manipulate your own draws. There is no server-side restriction on joining lobbies (free, private or championship); likewise for higher-ranked L0000 rooms. Games can also be stalled indefinitely with relative ease. Tsumokiri can be identified in every game type.
With regards to no server-side restrictions on stuff, I've had 4 bots play in the C00112233 JPML pro tournament momentarily: screenshots; game log; 2ch postings. Other really weird stuff is possible, too.

What is rate?
Rate is an additional ranking after the dan system. It is generally a better measurement of skill, and is a requirement for some tournament types and the upper-dan room. Keep your rate high. The base is 1500.

What is 3man?
3man refers to Tenhou's 3 player game mode, in which only 3 people play. There are some rule differences.

What resources should I link other people to for introductory purposes?
How to play: http://guide.riichi.nl/reachmahjong/intro.htm or one of the other tutorial links in the resources section.
Reference: http://www.ofb.net/~whuang/ugcs/gp/mahjong/mahjong.html with no exceptions. Stop linking other pages.
Tenhou information: http://arcturus.su/tenhou/

General Advice

• Tenhou uses Japanese rules. Not Chinese, or any other variation. If you know some other type that isn't Japanese, don't play on Tenhou; Japanese is very different to pretty much all others. Relearn the game for Japanese rules before playing: it will be different.
• Don't propagate false information when trying to get somebody into the game. This only causes confusion. Tom Sloper's website, for example, is excellent for general mahjong information, but garbage for learning how to play Japanese mahjong. Use some of the resources linked to on this page when trying to get information.
• If you find something wrong, contact me. Don't fix it yourself and redistribute it. This page is the main English resource for Tenhou, so it is no help in redistributing bits yourself. Steal everything here and redistribute it, calling it your own; just make sure you copy and steal everything. Incomplete stuff is useless to everybody, and it's easier to have me fix things.
• If you create or write something relevant, contact me and I will gladly host it.
• If you don't know how to play Japanese rules, don't play on Tenhou. People hate it when a player doesn't know what he or she is doing.
• Don't just pick the top left game type. Nashi rules are not friendly for beginners and people who normally play it are serious about playing it.
• Play as quickly as possible. It's alright to use the time available, but only use it if you have to. Stalling drives everybody mad.
• If you are a slow player, don't play in the fast game rooms.