Tenhou comes in various clients. Two kinds at the moment - a Flash version, played in a web browser; and a native Windows version, which uses fancy pants DirectX effects and has a lot of aesthetic differences. All the screenshots in this documentation are from the Flash version because the Windows one costs money.
Tenhou is found at http://tenhou.net/, where you can play Tenhou through your browser or download the Windows client. The Windows client is very similar, so the content of these documents will almost always apply to both the Flash and Windows clients.
Tenhou uses a mouse to control it. You click buttons and stuff happens accordingly, as it so happens. Keyboard control is possible by navigating the tiles with <TAB>.
Tenhou allows you to spectate ongoing upperdan games (観戦) or play games yourself (PLAY). The links beneath the buttons seen below open the client in the same window, whereas the buttons open a popup window.
On the following page select "connect to server" (サーバに接続) to load up the Flash client.