The sensor you mention has been discontinued and replaced by the GP2Y0A710K0F. The sharp website says they are comptible except for mechanical issues.
So, the datasheet for the GP2Y0A710K0F will be useful and can be seen here:http://document.sharpsma.com/files/GP2Y0A710K0F_DS.pdf
There are a few things to note:
1) The output is a straightforward analogue output, so reading a distance measurement is as simple as connecting the output to one of the ADC pins on the Arduino and reading the value.
2) The output is non-linear. If you look at Figure 2 on page 5 of that datasheet you will see the output voltage for measured distances. If accurate distances are required you will need a way to compensate for this non-linearity. The second graph shows the output for 1/distance is pretty straight, so this may be ok.
3) The output doesn't cover the whole 0 to 5V input range of the ADCs meaning that you won't get much resolution. This may be ok, it depends on your application, but the best way to solve this is with an op-amp or two to provide offset and gain.
4) The sensor can't differentiate between distances less than about 80cm and those more than that. What distances are you looking to measure?
5) Although the typical supply current is spec'd at 30mA, the "Advice for the power supply" section it recommends a fairly high power supply requirment of 350mA.
From the graphs, the gradient of the straight(ish) line is (0.01 - 0.003) / (2.5 - 1.5) --> 0.007.
Extending the line to the output voltage axis gives an offset of 1.15.
So a simple equation can be used to go from voltage to 1/distance . . . 1/d = (V - 1.15) * 0.007.
The reciprical of that gives the distance. A few numbers plugged in shows it is close-ish.
So the code without external op amps would be to
1) read the ADC (several times and smooth if necessary)
2) Do the sum.
I hope this helps a bit.