Getting it installed.

First download and install the addon from the Blender Market.  After this it will show up in User Preferences, Addons tab, Mesh category with the name "FastScale".  Enable the addon by ticking the checkbox on the right and if you want click "Save User Settings" to make the addon permanently enabled! If you wish to choose a hotkey to start FastScale: In the Input section of User Preferences at the bottom of the 3D View > Mesh section click 'Add New' button. In the Operator Identifier box put 'mesh.fastscale'. Assign a hotkey.  Save User Settings.

Using FastScale.

The addon will show up as a button named "FastScale" in the "Tools" tab of the panel on the left of the 3D View (press 'N' to make it pop out).  Click this button and the tool will be activated.  Now click in the 3D View on the spot where you want your scaling operation to start.  Keep the mouse button down and drag.  Drag in the direction you want to scale in.  First you'll notice nothing happens, this is because FastScale has a "kick-in" distance of 100 pixels (can be changed in Addon Preferences) before anything starts to happen.  When going beyond these 100 pixels, the selected mesh components (or the whole mesh when in Object Mode) will start to scale parallel to the view in one axis in the direction you have chosen.  Drag further and you will be scaling up, drag back to be scaling down (that's why the kick-in distance is there, it allows scaling down).  Press and hold the SHIFT key to restrict movement to the current axis.  Let go of the mouse button to complete the operation.  The kick-in distance can be changed to another value in the addon's preferences (User Preferences -> Mesh -> FastScale and click the arrow left of the "FastScale" name to see this setting).  The higher you set the kick-in distance, the lower the mouse sensitivity of the FastScale operation will be (you'll have to move the mouse further to have the same effect). That's it!  One more thing, you can enter a numeric scaling factor using the keyboard while dragging the mouse. Enjoy!