The side menu you can see on the demo site uses the extended menu module to achieve the mainlevel and sublevel styling.  Positioned in the left or right module positions and given the attribute of a flat list - any menu will behave as you see it here.

In order for the drop down menu to have child items (eg items that are sub menu items of the main navigation items) you will need to set the menu accordingly in the Joomla backend. 

1. In the back end of Joomla navigate to menu ---> main menu (or the name of the menu you selected in the previous step.

2. Create the new menu item as per the usual method. eg choose whether you want it to be a url link, component link, blog category link etc.

3. Write the name of the menu item.

4. Publish the menu item.

5. Set the parent item for the menu item. So if you want to have the menu appear on the main level of the menu then dont select anything here or make sure the menu item is set to top. If you want the menu item to be a sub level menu item then simply select the menu item that already exists that you want the sub level to appear under.

6. Configure any other options that may be relevant for your menu link.

7. Click Save.

The next step is to set the extended menu module parameters to the following:

1. Menu type - flat list

2. Expand Menu - Yes

3. Menu Template - No