The glass is attached to the regulator with a square piece of white plastic you've mentioned. Prob the broken bits you have?
The white square of plastic is on the regulator itself and is the bit that moves up and down the regulator moving the window.
This piece of square plastic attaches to the bottom of the glass by way of an aluminium channel which is on the bottom of the glass.
On the bottom of the aluminium channel there is a small black plastic clip which needs to be removed, this allows you so slide the white plastic bit out of the aluminium channel - thus seperating the window from the regulator.
When you have the new regulator, this piece of white plastic just slides back into the aluminium channel on the bottom of the glass - and is heldin place by putting the black plastic clip back on.
If you've not already done so, you need to drill out the 5 or 6 rivets holding the regulator in place. I manually moved the window down and secured in place with tape before taking out the black clip and sliding the white bit out of the aluminium channel.
Once you've done that you have seperated the two parts and you should be able to wiggle the regulator out of the door, it does have a small hook to keep in place by the top rivet, but it should lift free. Unplug all the electrics first of course.
Putting the new one is the reverse of the above, you need to slide the square white plastic bit on the new regulator into the aluminium channel on the bottom of the glass - and put the black plastic clip back on to stop the two bits seperating once you move the window up and down.
Once it was all back in place, I plugged the electrics back in to test before putting any rivets back in!
I didn't use a new bit - managed to pick one up on e-bay cheap. In good nick, no rusty wires etc. Seems to work fine.
Not very techinical - but may help you.