How do I delete the artboard and only keep the object?

For example - I open a new file in Inkscape (white square art board) and make a circle in the middle. What do I need to do in order to _only_save the picture and get rid of the white background?

So, I´m now trying Inkscape (after using Illustrator) and have encountered some frustrating problems. I have two Inkscape files, and I want to copy/cut out a object in one of them and move it to the other file. Problem is that when I cut out a object it doesnt come alone, but with a white square aro...