To expand on my previous comment, and address your particular use case, I will cover both the shape keys and the animation to achieve the effect you are after.
You will first subdivide your plane sufficiently in edit mode. Next, in object mode add two shape keys from the object data context in the properties window.
Tab into edit mode again, and enable proportional editing with O then select the central vertex of the plane and move it down the Z axis as far you would like while adjusting the proportional edit influence with MMB.
Next, return to object mode and make sure you are on frame one, then move your sphere to it's starting location, and add a location key frame by pressing I. Then go to your shape keys, you will notice under your second shape key, named key 1 by default, it has a slider with a value from 0-1. 0 being the basis, or original shape, and 1 being the modified shape you made in edit mode. With your mouse hovered over the slider, drag the slider to 0, and add a key frame with I
Now, jump ahead in the timeline to where you want the animation to end, to better judge the rate of fall for the sphere, first add a new key frame for the plane's shape key at a value of 1 and play through the animation to see where the plane begins to deform so you can judge which frame the sphere should make contact with the plane. From here, you can move the sphere to meet the plane at that specified frame, and key a new location keyframe, then another at it's final position.
When you play the animation, you may notice that the sphere moves a little too fast, so what you can do is split your window, and go to the dope sheet. Locate the key frames for the sphere, it will be titled SphereAction by default.
You can then drag individual key frames forward or backward along the timeline with RMB, and make any adjustments needed to your timing. When you're happy with everything, add your textures/ materials, and render!
A rough example of what you should be able to come up with following these steps is as follows: