Q:

Creating a hill out of a plane

Is it possible to grab a group of vertices and pull them upwards. And instead of the having just that area go up, can all the other vertices move in a beautiful manner (don't know how else to explain it)? 

A:

What you're looking for is called proportional editing. It allows you to select a point or set of points, and when you move those points other nearby vertices will move along with them.
To use proportional editing, enter Edit Mode by pressing Tab, then look on the bottom of the window and enable Proportional Editing (you can also use the hotkey O while in edit mode to toggle proportional editing).

To the right of that menu there is the Proportional Editing Falloff menu, which lets you select how nearby vertices will be affected.

Once you have proportional editing turned on, select a vertex and move it, and the nearby vertices should move along with it. To broaden or narrow the effect, use the mouse scroll wheel.

Images are courtesy of the Blender Manual and the Blender Wiki.

