In addition, you can tell whose turn it is by looking at whose clock is ticking. The side to move's clock is displayed in blue, constantly ticking down. The other side's clock is displayed in black.
The side to move actually has two time numbers shown: mm:ss > MM:SS. The left mm:ss is the time left (minutes and seconds) at the start of the turn. The right MM:SS is the time left (minutes and seconds) now. Be aware that this is only an approximation of the time, not corrected for lag.
When you submit your move, there may be a noticeable lag time before the server's acknowledgment arrives. During this time, the board position and SIDE TO MOVE display will reflects your move, but the clock display keeps decrementing the clock on your side, with the notation (lag=MM:SS). If you are using TIMESEAL, then the lag time will not really be counted against you; if you are not using TIMESEAL, then up to that amount of time will be subtracted from your clock.