Start by opening the User Preferences (File > User Preferences…)
Go to the “Add-ons” tab in the top menu.
Press “Install from File…” at the bottom of the window.
This will bring up the file browser, locate the file you received when downloading the add-on.
Select it and press Enter, or “Install from File…” at the top left.
Find EasyFX amongst the other add-ons by either searching for it or locating it in the “Render” category.
Tick the box to the far left of the add-on, this will enable the add-on.
Press “Save User Settings” if you wish have the add-on enabled by default when you launch Blender, otherwise you’ll have to enable it each time you want to use it.

Once the add-on has been installed you can locate the EasyFX panel in the Image Editor.
When previewing the rendered result in the Image Editor, press T to bring up the left toolbar, switch to the tab that says “EasyFX”.
From here you can start enabling effects by checking boxes and changing values.

In order to have the image keep updating automatically, make sure you have “auto update” ticked. If you wish to make changes then update the image manually, simply untick “auto update”.

Some effects may require you to re-render the image. Example of those effects can be: Cel shading, transparent sky, image sky, motion blur, depth of field etc.

IMPORTANT: The post-production has to be done before rendering the animation.
Render a still frame of the animation and start doing the post-production.
Once you’re happy with the results you can start rendering the animation and the effects will automatically be applied to each frame.

In this tutorial Grant goes over how to install and use EasyFX. He goes over what most effects do and how to use them.