Keep it clean. Rub it with a cloth after every time you use it. Well, that may be a bit obsessive actually. Just keep it clean of all obvious dirt and dust accumulation. Store it in a dark dry place.
Sunlight can dry it out like an old lampshade.
Store it rolled into a loose coil along its natural bend. Don't force it to coil any tighter than it wants to. However, it has been my experience that most people use far too much oil on their whips and this is as bad as using water and will rot the leather at the end about four inches from the fall. The other problem occurs when people use whips around wet grass etc. Remember, neet's foot oil can be great for leather but use sparingly on dry whips only.