Open the application on the desktop you want it to appear on.
Right click the application window's top border/header. Choose Advanced --> Special Window Settings. In the pop up window, the first item is Position, to set where the window opens on the desktop. Sixth item down is Desktop, which defaults to the current desktop. Put an x in the box, then use the now activated drop-down menu to choose the actual way you want the window handled. I usually choose Apply initially, but you can play with the others to see what difference they make, if the choice is not self explanatory.
There are other selections to further specialize how the application appears when first opened. Play to your hearts content.
