For the most part, to navigate menus in OS X you simply click one with your mouse and then click the desired command from the menu. While this is the most straightforward option for accessing what you want from menus, there are some alternative approaches that at the very least might be good to keep in mind, but with practice may even be quicker than grabbing your mouse.
The first of these is the use of arrow keys, where by pressing up and down you can change the focus to various items in a given menu, and press left and right to change menus either along the top menu bar, or to open or close a submenu.
The second is to use page-up and page-down (hold the Fn key and press up and down if your keyboard does not have dedicated page up and down buttons). These keys will jump the menu selection to either the first, or last selectable options in the menu.
A third option, which might be most handy if you have a large menu open, is to navigate it alphabetically by typing the name of commands or other items that are active in the menu. In this way, you can quickly jump to the command by typing only a few characters of its name. While this might be less optimal for smaller menus, an instance where it might be useful is if you have a large number of files open in a specific program and are using its Window menu to locate one of interest. If you know the file’s name (and hence its window name), then you can go to it by opening this menu and typing the first letters of its name.
Similar to typing the name of commands, you can also use the Help menu’s search feature to locate specific commands in any menu. When you do this, OS X will display the menu item with a large arrow indicator that points to it.
Finally, as with many other features in OS X, pressing the Escape key will cancel the current action, so if you have a menu open and wish to close it, then along with other options you can press the escape key and it should disappear.
Some examples of using these are the following. Note that while I’ve use the standard “control-F2” hotkey for focusing on the menus, I recommend you change this in the Keyboard system preferences to be something like Control-Option-Left Arrow (or Up Arrow) as it may be easier to remember.
To navigate to a window with a known name, just do the following:
control-F2 > "Win" > down-arrow, Space, or Enter > "type letters of window name" > Enter
To get to the Help menu and search for any command:
control-F2 > "Hel" > down-arrow, Space, or Enter > Start typing your search
To get to the About This Mac window:
control-F2 > Down Arrow > Down Arrow > Enter
While these options so far have applied to the system menus, they work for most other menus as well, including Application menus in the Dock (which you can set in focus by pressing Control-F3), and some of those within applications that can be opened by using the Tab key if you have full keyboard navigation enabled in the Keyboard system preferences (toggled by pressing Control-F7).