Using The Transform Panel
Toward the bottom of the Right Panel in the Develop Module you will find the Transform Panel and you can do some pretty neat stuff from within this panel. In my opinion, this panel should be grouped with, or at least near, the Crop Panel as they both effect the size and shape of your image. I find I rarely use the Transform Panel for my landscape photographs but it is tremendously helpful for urban or architecture photography. The panel holds the best ways to correct different forms of distortion that can regularly occur when photographing straight lines. With the images below I'll demonstrate what the different options and sliders of the Transform Panel do to your image. In these images I DO NOT have "Constrain To Crop" on but when performing these tasks you should have that checked - the white areas in the images would then be cropped out. (Tap the images to make them larger)
In the images above I have the original Image on the left and on the right I have clicked on the "Auto" option of the Transform Panel. When you click the Auto button Lightroom applies a balanced combination of all the other options in the Transform Panel. Many times, as in this demonstration, it is a very subtle change.
Demonstrated above is the use of the Guided function, which I find to be the most useful function in the Transform Panel. With this function you draw lines across what lines should be perfectly horizontal and perfectly vertical. You can place up to 4 guide lines - representing vertical level, horizontal level, the x axis and the y axis.
Demonstrated above is the Level option and you can think of it as the Auto-Straighten option and the results, like above, could be potentially minimal if your image started out relatively straight.
Above is the Vertical option and this corrects for Level and converging vertical lines - again, not always a dramatic effect.
The final "button" adjustment is the Full option and this can have a dramatic effect on your image. This applies a level and converging - horizontal and vertical - lines correction.
Above is a demonstration of the Vertical Slider and as you can see adjusting this slider will "stretch" the image. You can think of it as rotating along a horizontal axis in the middle of the image while stretching the image.
The Horizontal Slider, demonstrated above, is quite similar to the Vertical Slider. The image will stretch and rotate on a vertical axis.
The Rotate Slider will do just what it says. Depending on which way you move the slider the image will rotate to the left or to the right.
Above is Aspect Slider and this will change, naturally, the aspect of your image - making it narrower or wider depending on which direction you move the slider.
You can enlarge or shrink your image by using the Scale Slider.
Finally, the X Axis slider will move your image left and right. while the Y Axis slider will move the image Up or Down.
And there you have it, the Transform Panel. Go ahead and experiment with it a bit - it can be fun! Remember everything you do can be undone in the History Panel or by using CMD/CTRL + Z keyboard shortcut.