Sorry if this is a really basic question, but I don't use Poser much and never had a need for this. In Poser 2012, how do I render an image with a transparent background, as in just the object and not the default grey behind it? Thanks for any help.

Render over black (in the render options), then save it as a png or tiff.

Png will save it with a transparent background.

Tiff will save it with a transparent background and the alpha channel info.

You will need to make the ground plane transparent depending on the angle of the camera as well.

Select the ground. Go to material setting advanced tab.  Make sure "shadow catch only" is checked.

If you don't want to render the ground shadows, select the ground. Go to properties, and uncheck "visible".

I don't think you need to change the background color. But I often do change it to match the color of the destination background (if there is one) just in case there's a bit of a fringe.