First, make sure that you are clicking down on the tab for the eraser component before inserting the eraser refill. If the tab is not clicked down, you will not be able to fully install the eraser refill. Insert the side with the little plastic rod first.
While holding down the eraser component tab, insert the eraser refill all the way until it stops.
The new refill should stop with a little bit of the eraser tip left out, when the tab is still clicked. Now you are ready to start erasing again!