Please provide a part number or link to a data sheet (once you can post links).
What is the repetition rate of the ultrasonic pulses?
Did you want to record the length of the echo pulse for each repetition?
You've already figured out most of what you need to do - count the length of the pulse. To do that, you need to receive the pulse on a pin, synchronize it to the 50MHz clock (using a cascade of two D flip-flops) and then use that as the enable to a counter. The first pulse you get will cause the counter to count up. If you also create logic to detect the falling-edge of the pulse, you could copy the count to a RAM location. You could record multiple pulses, and then read them out, or average them, or ...
If you can control the pulse repetition rate, then you could enable the sensor to generate a pulse, wait for the echo to be counted, read the counter value, clear it, and restart.
You can control your logic using the JTAG interface on the DE2 board. See this tutorial:
http://www.alterawiki.com/wiki/using_the_usb-blaster_as_an_sopc/qsys_avalon-mm_master_tutorial Cheers,
Dave