How do I implement a communications interface to an Altera FPGA?
It depends on how much bandwidth you need, because you will need to write software on the other side to collect your data. You will probably also want to minimize the IP or HDL code you have to write on the FPGA side.

The easiest thing would be to use a uart to USB as most software has compatibility for serial ports but you are limited on bandwidth. On the FPGA side there is an RS232 UART core under the university program.

USB is going to be more complicated as you will need to write a driver on the PC side and on the FPGA side you will need to have a USB core. Both of which have a significant time investment to implement.  

You can also use the USB blaster to send information over JTAG into a quartus debug terminal, and I believe that you can also use the uart over this interface, but if you already have an RS232 to usb on the board, that would be easier to use.

I don't need the bandwidth so I implement an RS232 port on the boards I use, if I need more bandwidth, I use a quad spi interface to usb by FTDI.