I've been using this brush now for over a year and here's my way of cleaning a group.
Fill a pitcher with hot water
Add some cleaning powder, you can even use the same solution as you do when you clean your portafilters.
Load up the brush by dipping it into the solution.
Insert the brush into the group as you would a regular portafilter.
Here is a close-up of the brush inside the group. As you can see it fits exactly over the rubber gaskets and is able to clean up around the gasket and the bayonet ring. A lot of coffee oils and grounds live up there.
What I do then is take the brush out and dip it again in the cleaning solution - you will then see how much dirt and oils there were inside your group.
To finish I then rinse the brush under the tap to clean it, I then do a final clean of the group with the clean brush. I then use a wet micro fiber cloth and wipe the entire area.
Your group is now clean!