The warp modifier deforms a mesh as if some force acted on it. The force starts at the "start" object and ends in the "to" object. The "start" object center and the radius determine which vertices are affected. The texture option has an effect similar to the texture of the displace modifier.
You need to increase the radius in order to see something, because there is no effect if the radius is smaller than the distance from the source. The scale and rotation of all three involved objects does matter (even if the "from" and "to" objects are empties), so it is best to apply the scale and rotation before playing.
Also note that the manual uses a grid, not a plane without subdivisions.
I found this tutorial useful: https://www.youtube.com/watch?v=AzMVZa5OVBY