I, too, have some of these drivers and some 3 Watt LED modules.
It's odd that there is no documentation for these drivers anywhere on this site.
I looked up the "C310" marked on the IC on the little board and found a likely suspect by searching the web. It's likely that this is a Zetex ZXSC310.
Based on the datasheet for that IC, and tracing the little board, I came up with this as a schematic for the driver board:
Based on that schematic, the only way I could imagine the board working was to connect the LED module between terminals A (positive) and B (negative). Then, the positive side of the power source is fed into terminal D (which is electrically tied to terminal A on the board). The negative side of the power supply is tied to the "ground ring" which I've called terminal C.
This results in a hookup as shown here:
Connecting things this way, the unit seems to begin lighting the LED with about 2.3 Volts applied. The brightness of the LED seems to max out when the input Voltage reaches about 3.3 Volts. From that point upwards, the brightness appears to be reasonably well regulated. I stopped at about 8 Volts because the datasheet for the ZXXC310 states that the maximum voltage for the IC is 8 Volts.
I'm not sure where advertised voltage of 12 comes from, but I wouldn't exceed 8 Volts, and it's probably best to stay a bit below that for a safety margin.
I also think the wiring setup I've arrived at here makes sense because when used in a typical flashlight, the module would be mounted so that the positive "tip" of an AA battery could contact the center circular "pad" on the non-component side of the board and the barrel of the flashlight would contact the "ground ring" that surrounds the board on both sides. That would allow easy mounting in a flashlight while allowing contact to be made easily.
Then, on the other side of the board (the component side), the connections could be taken off of the small solder pads for wires actually feeding the LED module. At least that's what makes sense to me.
Again, it's unfortunate that there is no documentation supplied with these modules and that there is no documentation for them on this site. I would not have purchased these units had I known that no data was available.
Anyhow, that's what I've figured out on my own, but I'd still prefer to have the actual data from the designers.
The LED modules are straightforward and operate the way I'd expect when driven from an adjustable power supply. Setting the current limit to 750mA gives a very bright output as expected. When connected through this module, wired as I've shown, the drive seems reasonable, with the circuit limiting the drive current over a fairly wide range of input voltage. For a flashlight, this setup would run best with, say, three or four 1.5 or 1.2 Volt cells in series, or, perhaps, two Lithium cells in series.
I'd really like to see this site's administrators step in here with the real data for these devices, but until then, I hope this information is of some help.