Can anyone provide me with a Gaussian blur Effect Class?

Its easy to use a effect using the pipeline tool you basically just double click it (Content.mgcb) in visual studio to open it up. If you get a xml file that opens up instead of the tool executing then use “open with” or set the default visual studio uses to open it.

from there you should see the pipeline tool open up.

http://www.monogame.net/docs/html/images/pipeline.png

You want to edit → add a new item and pick effect.
http://www.monogame.net/documentation/?page=Pipeline

From there using a hlsl effect is pretty simple here is a example i made a while back that uses a custom effect with spritebatch most of that is irrelevant but it shows how to load and use the effect as well as how to pass globals to it ect.

Using one of the shader examples posted by others above should be pretty intuitive from that point.