Basically, what it is saying is that your interface has to:
1) Wait for SOS (start-of-scan) line to go low (for what looks like 2 pixel clock pulses). When it goes back to HIGH...
2) Wait for 32 pixel clock (PCLK) transistions (count the transitions as they happen on PCLK)...
3) On the next PCLK transistion, read pixel 1 (via the analog output pin SOS).
4) Continue reading (2047 more PCLK transistions) to read the rest of the pixels.
Basically, your interface reads PCLK at a particular rate (as set by ps0,1,2 - you can specify an internal PCLK, or an external one if you want to control it with an oscillator or by other means), and you read the data out per clock pulse as specified by the timing diagram.
For the Arduino and using the internal PCLK, I would tie the PCLK line to an I/O pin that can sense an interrupt, then fill a buffer in the interrupt handler (though you would have to skip some pixels, if you are sampling the analog voltages - as there wouldn't be enough space for that many values).
I hope this helps you to understand how this device works (BTW - SH and SHUT lines I think control when to scan, and whether the output is an analog level value or (digital b/w?))...
BTW - remember your 50K pullup resistors on the input pins!
This would actually be an interesting sensor to use for a laser distance measuring device aka LIDAR (triangulation-based - not time-of-flight).