OTG adapter I have is a specific type for the Samsung Galaxy Tab 2.
The GT2s use a proprietary plug .. not a micro USB type.
The handy part about it tho is that it has both a USB port and two card reader slots(1 microSD and 1 SD). There's a switch to choose between USB or SD usage.
Very handy (overall) as you may sometimes simply want to read data of another card of some type.
Plug the camera into the USB port(in USB mode obviously) and it comes up as a mass storage device, like Frank said.
Plug the SD card into the card reader(in SD mode) ... etc. etc!
For software, my preference has always been ES File Explorer .. although in saying that I've never tried Astro.
Only in the past few updates, they have added some, and it's looking more likely I'll go back to X-plore.
EDIT: my OTG adapter is similar to something like this one on ebay.
http://www.ebay.com.au/itm/New-3-in1-OTG-Adapter-Connector-Card-Reader-SD-Micro-SD-USB-Mobile-Phone-PC-/151555829330?hash=item23496e6e52:g:Dp4AAOSw1vlUujZ2ps. I have no affiliations nor history with this seller .. just posting a link to what my USB/Card reader OTG device is almost similar too. Mine doesn't have the cable connection and is directly attached. Sometimes it feels a bit fragile, so maybe a cabled connection could be a safer long term proposition.