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.

With this menu open, simply typing “To” brings me to the “To Do” item, which in this case is my list of tasks for the day, among the myriad of other TextEdit documents I have open.
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).
The fastest way for me is to press the Help shortcut (CMD+?) and type the menu item, than press enter key.
There’s a typo in the instructions “To get to the About This Mac window:”. They should start with control-F2, not command-F2.
Yikes! Thanks! It’s been fixed!
There seems to be an issue with control-F2 not working sometimes. I am seeing it on a Mavericks machine only, not a Snow Leopard machine.
A Google search revealed that others had experienced similar inconsistencies, but that immediately preceding control-F2 with a control-F3 gave the desired results.
Sometimes people might have software installed that overrides built-in commands. At other times, people might have disabled these in the Keyboard system preferences, or re-used them for other purposes.
That doesn’t seem to be the case with my machine. The fact that preceding the control-F2 with a control-F3 enables control-F2 temporarily indicates control-F2 is not remapped by something else. Of course there always could be an unintended interaction with some other software, but in my case the Snow Leopard & Mavericks machines have basically the same software and add-ins. Also it is not disabled in System Preferences->Keyboard->Keyboard Shortcuts, nor is it remapped in any other Shortcuts there.
Furthermore, just as others have reported, the problem has at least temporarily disappeared after a reboot. It will be interesting to see if it reoccurs…