Hello,
I didn't use audio codec with Altera, thus I can give only general hints.
You guessed right, that you need a serial-to-parallel conversion of AD data respectively a parallel-to-serial conversion of DA data. Common codecs use I2S standard for data interface (don't know if you have DE2 or Altera DSP board). Additional you have to setup the chip through control interface, which can be either I2C(DE2,Altera DSP) or SPI(only Altera DSP). In your case, you would choose 16 Bit data length and your preferred sample rate.
I wonder, if Altera has shipped any design examples with DSP board. Terasic has audio "demonstrations" with DE1/DE2, but they are far from being instructive to my opinion. Just a few naked lines of verilog code.
I could be a good HDL programming exercise to build the codec interface from the scratch, using only the codec datasheet, but probably that isn't your main interest.
Regards,
Frank