Creating a new Joomla! menu

Login to your Joomla! Site Admin (www.yourdomainname.com/administrator)
Use the top menu and navigate to Menu(s)>Menu Manager
Click New in the top right
In lowercase, with no spaces, enter a Menu Name (Unique Name in 1.5.x)
Enter a Title and Desription, usually similar, ex:Bottom Menu (only in 1.5.x)
Enter a Module Title (this is the title of the new menu module that will automatically be created)
Click Save in the top right
Now you'll see your new menu in the list
Click on the Menu Items icons for your new menu (hover and "Edit Menu Items" will show)
Alternatively, you can use the top menu and navigate to Menu(s)>bottommenu (or your new menu name)
Add your new links to this menu (click New in the top right and choose the menu type, etc.)
Read more about creating menus here (coming soon...)
Now that we've created a new menu, and its menu items, proceed to Modules>Site Modules (Extensions>Module Manager in 1.5.x) in the top menu
In the filters on the right, -Select Type-
Select mod_mainmenu
This is Joomla's core menu system and confuses many, because this will actually find all menus, not just the main menu
Find your new menu Module Name (Bottom Menu in our example) and click on the title to edit
Choose it you'd like to Show Title (will display a heading over your menu)
Choose Published (Enabled in 1.5.x)
Under Pages/Items (Menu Assignment in 1.5.x) choose the pages you'd like this new menu to display on (All by default)
In 1.5.x, if you'd like to choose specific pages, first click "Select Menu Item(s) from the List
Hold Shift to and click 2 items, and all between will be selected
Hold CTRL (clover on Mac) and you can select multiple items
Choose your Menu Style to decide whether you like an Unorder List, Vertical, or Horizontal menu
The best option here is a Flat List (List in 1.5.x), and the usage of CSS to change how this list is displayed
The easiest option for beginners is Vertical or Horizontal, but this will produce a table instead of a list
Click Save in the top right