Reading ADC using Altera DE2 Board (Beginner)
What kind of data am I reading?


Similar to SPI.  The datasheet details it.


Where/how do I connect it?


Absolutely anywhere. It's up to you to designate what pin is which on an FPGA (within limits).


Is it possible/feasible for a beginner


Yep, shift register systems are pretty simple to implement.


...use Verilog HDL or MIPS Assembly Language


You could do it entirely in Verilog, or tap up OpenCores for an open source MIPS IP to drop in to do the processing side of things for you.