The Versus Recorder can only be used to save battles when you Battle in the Battle Frontier or when you battle someone else either through DS Wireless Communications or through Wi-Fi.
After a battle, they will ask you if you want to save the battle or not, pressing A will allow you to save it on your Vs. Recorder. You may only save one battle video at at a time, saving another will replace the older one.
*Also, l believe you can download videos somewhere, l actually forgot where, and l'm not even sure if you can download videos on your Vs. Recorder, but l think it goes under the "Other Videos" category. ~