Navigate folder structure in Open/Save File Dialog with keyboard?

Solution 1:

System Prefences > Keyboard > Keyboard Shortcuts > Enable "Full Keyboard Access: All Controls", then you can use Tab to move between elements until your file list is highlighted, and use the arrows to select your file, in fact you should immediately be able to type a letter or use the keys as the default focus should be on the file list.

Solution 2:

File dialogs should support the same shortcuts as Finder.

You can also press ~, /, or ⇧⌘G to open the Go to Folder sheet.

If Full Keyboard Access is enabled (in the keyboard preferences), ⇧⇥ moves focus from the file browser to the source list.