wrote:

I'm trying to build my first home-build computer.(Asus A7N8X-E)
And now I have a question about how I do installing my MoBo in the
case.I have fit those copper things to keep the distants between
the case and the MoBo.

The distance is so that the underside of the mainboard does not
contact the metal case.

On the MoBo side I have to fit these little ring for the electrical
insulation (or is this isolation!!!)
Whatever, my question is::do I fit those rings on both sides, or
just on the top side of the MoBo.

Maybe neither. Did you get those rings from some shop?

Modern mainboard's are designed to be grounded at those points (I'm
not saying it's absolutely necessary).

http://usa.asus.com/products/mb/sock...7n8x-e-d_l.jpg

In the picture, you can see silver colored electrically conductive
circles around the mainboard mounting holes. Those are ground
points, they are connected directly to device ground pins on the
mainboard. Power supply and mainboard ground are connected to the
case. There's no reason to insulate those points. Of course you
might want to avoid overtightening the screws or using screws which
have very big heads.