Calc is much clumsier than Excel in this regard. You can only drag areas which are highlighted (black); you drag them by clicking and dragging the black area.
The trick with a single cell is to get it selected: you have to click, drag out of the cell (now two cells turn black), then drag back into the first cell, and now you have a single black cell you can drag to another location. Remember to drag by clicking in the black area, not on the border like Excel.
You can also click on the cell, then Shift+click to select it (black), then drag it--but it's easier just to do it all with the mouse, since you're going to drag it anyway.
Edit: Note: OOo version 3 or later uses a transparent blue highlighting, instead of the plain black, reverse video-style highlighting.
Found here: https://forum.openoffice.org/en/forum/viewtopic.php?f=9&t=12466
You can also click on the cell, then Shift+click to select it (black), then drag it--but it's easier just to do it all with the mouse, since you're going to drag it anyway.
Edit: Note: OOo version 3 or later uses a transparent blue highlighting, instead of the plain black, reverse video-style highlighting.
Found here: https://forum.openoffice.org/en/forum/viewtopic.php?f=9&t=12466