Drag video file into HandBrake

On the Summary tab:
--click Web Optimized

On Video Tab:
--change frame rate to "Same as Source"
--Click the radio button for Constant Frame Rate
--Set the Quality to >35 RF (usually 40)
--Under Encoder Options: set the slider to VerySlow

Click Browse in the bottom right and assign an output filename.

In the top Menu Select the Green Encode Button.

Also View the ScreenCast here to view the above instructions in action:
https://www.youtube.com/watch?v=sgmE1T8A4UY