Gameplay is easy and intuitive, so most of this is just screenshots and brief descriptions. The gist of controls is click regular tiles to throw them, captioned tiles to call or the popup buttons to declare ron, riichi, tsumo, nuki (3-man) or pass. There are also some auto-buttons below your hand which will be described.
Your hand is presented as shown above. Drawn tiles appear spaced to the right of your hand while all the tiles are auto-arranged. To throw a tile you click it. If you can throw it at the time it will be green, otherwise red (e.g. it isn't your turn). The numbers next to the far right tile are the time you have to make your move. The left number counts down from the default round move time, then the + figure counts down. The + figure is static throughout the round and doesn't go back up like the left figure does. When it reaches zero, you only have the round time (5 seconds for normal games) to make the move.
The board in the middle shows the players' respective ponds and statistics. Each side shows the player's wind (large wind kanji), alias (bottom white text), score (digital clock-like numbers), rank (green/white text to the right of each score) and sex (marker above score - blue for male, red for female).
In the middle there is the round information and indicators. The round is shown by the wind, round number and 局. Beneath that is the 100-marker indicator for east's player and the current riichi bets (they stay on between rounds if not claimed).
When given the opportunity to call and make a meld, the possible melds are shown in blue when hovered over. They are indicated by the type of move captioned above the specific tiles. In the above image チー (chii) is written above the different calls that can be made.
To make the call, click the respective captioned tile. To pass, press the popup パス (pass) button. These moves also have time limits and the static bonus time will also go down.
Different popup buttons come up at different times. When you can put yourself in closed tenpai, Tenhou gives you the opportunity to riichi with the リーチ (riichi) popup button. You can not riichi by ignoring the button and playing normally.
There are other types of popup buttons also. See Call Types.
When calls are made the type comes up in large letters contiguous to whoever called it. In the above image west is calling a pon (ポン). The same goes for all other calls, including riichi, ron and tsumo.
You can be presented with more than one popup button. In this case you decide what move you want to make. The above image shows a ron (ロン) opportunity. It can be called by pushing the ロン button, or skipped with the パス (pass) button.
When hands are called Tenhou throws up a window with the hand at the top and the finishing tile highlighted. Below is shows the top of the dead wall with any flipped dora indicators. It dramatically lists the yaku and bonus names with adjacent values. At the bottom, if the caller was in riichi, it shows the dead wall's ura dora (裏ドラ). It then states the fu (付) and han (飜) followed by the final hand value. If it is a limit hand it will also state that. In the above image it is a mangan (満貫) hand. Below that it shows the indicators and bets and the exchange of points. Press OK to play on. If the game is over it will say END instead.
For a list of all the possible han, see Yaku. Also see Limit Hands.
The three bottom right buttons (cruise control buttons) that only show up in gameplay are, from left to right:
The last part of gameplay is knowing when you are in furiten. Tenhou is helpful and tells you when one of your waits is furiten and also when you are in full furiten. Directly beneath your hand in the center Tenhou will display 「フリテン」 should you be in either. If you are in full furiten (all waits are furiten) it will be illuminated, otherwise it will be semi-transparent grey text. If you aren't in furiten at all it won't be there.