If you do some googling on various terms, such as:
...you'll find a few circuits (a good way to find them is to do a google image search, then back-search the link if necessary). For example, here's a PIC-based sonar:
You don't really care about the PIC portion of the system; you only care about building the transmitter and receiver portions. Note how simple the transmitter section is compared to the receive section? That's because you need to amplify and filter the received signal in order to be able to read it with a microcontroller.
Now - I am not saying that the above circuit is the "be-all-end-all" circuit, nor might it be the best. You're going to have to do some searching on this one. Essentially, you need to create an amplifier for the transmit side, and generate a 40 KHz signal with the microcontroller (Arduino in your case) to drive it. One thing I noticed about the above circuit was that it seemed to only drive the transducer in a single direction; these transducers should actually be driven by a push-pull amplifier, and many can handle quite a large voltage swing (in your case 10 volts RMS - or about a +/- 5V swing around 0 volts). Ideally, you'd want a way to move the transducer in this fashion, at the frequency needed (40 KHz). Moving it in only a single direction reduces its efficiency.
The receive section is the more difficult area to build (in all but the simplest schematics I have seen), but it is necessary if you want to be able to have good range and accuracy. Also - it is possible to build the circuit so that only a single transducer is needed. One place I found for interesting circuits of this nature (for their own transducers - so you may need to play a bit):
Here's some more info - you could probably adapt one of the circuits shown:
Note the strange "back-to-back" diode arrangement? That's the key to a single-transducer system...
Something else to keep in mind - although some have pointed out that it isn't absolutely necessary, having an oscilloscope and a frequency generator for development of ultrasonic ranging circuits can be helpful; but generally, if you can tune your code to generate the frequency needed, you're most of the way there (where the scope comes in handy is tuning the receiver and transmitter together to get the best signal; its possible to eyeball it for "goodenuff", though).