How to ground pins on a multilayer board with a ground plane?
It depends of your device. Ground routing is sometimes a black magic. ;)

And very often, on most complex circuits there are several grounds as well. 

But if your device is simple and plain digital, then yes, connect directly to the ground plain. That is why it is there.

On the other hand, few devices really need multilayer boards. In most cases with careful design you can use two or even one layer board for the same schematic.