When your Administrator has set up the Extension correctly you should be able to insert a content element of type "Nested Content Element" into a Column of your page. You can not select it from the Content-Element wizard - you have to create a content element of some "normal" type before and then switch the type to "Nested Content Element" using the "Type" select box at the top when editing the content element.
When you have switched the type to "Nested Content Element" next to the "normal" fields which show up for every content element (like Header, Top/Before, Index, etc.) there will be only one field labeled "Container template" there you have to choose one of the templates which your Administrator created for you (See section Configuration).
When you have choosen a container template just press the Save&Exit button and leave the content element editing screen. Then use the (traditional) Page module to view the page on which you created the container element.
You should now see a template with Content Areas which looks like you Adminstrator has designed it. There will be Columns with a "New content element" button like you know it from the normal columns: Left, Normal, Right Border. You can use this button to create a new content element or can copy & paste already existing content elements over using the new copy & paste buttons which became available after installation of this extension.
When you have installed this extension you still can copy & paste content elements around using the context-menu of an element. But it is a known problem that you have no way of inserting a content element into an empty column as there is no element whose context menu you could use.
To work around this behaviour - cause by using this extension you will have a lot more (empty) columns - each container is empty at the beginning - parts of the kb_pm_paste extension were incorporated into this extension and even improved (multilanguage copy&paste does work now). So you can use the newly available "Paste" button at the top of every column to paste an element into the top of it.
Your administrator can either have designed a template for you with a fixed number of columns in which you can fill in content elements or he can have designed one which allows you to dynamically add new columns to the container content element.
When you are confronted with such a content element with variable amount of columns you will have a button somewhere inside the content element preview (In the page module) which allows you to add a new content-area.
IMPORTANT: You can always just have ONE (!) column on the right/bottom side of a variable-column-section which is not filled with contents. This column will not get rendered in the FE as long as you do not fill content elements in. You can of course still have columns in the middle which are empty by cut&pasting the right/bottommost content element to the free column which is always next to the right-most content-element.