How does this Audio ADC know which rate to sample the audio at
If you look at Table 2, you'll see that the MD0 and MD1 pins control how the master utilizes the clock input (either 256, 384, or 512 * fs).  Once you select one of these options, you can use your crystal frequency to tell you the sampling frequency.

Once you know the sampling frequency, you can use the resolution to give you the BCK rate.  This particular part has 24-bit resolution.  Each "frame" of audio consists of two channels, left and right.  Each channel has a 24-bit value.  Therefore, each sample is 24-bits of data.  If, for example, you are using 64KHz sampling rate (by selecting 256fs using MD0 and MD1 pins), then you can get the BCK rate:

24 bits/sample * 64,000 samples/sec = 1,536,000 bits/sec

Therefore, your BCK frequency is 1.536 MHz.  Your L/R clock will be 24 times slower than this, since it oscillates when the channel switches, which is every 24 bits.