move forward and backward by one word

In a GNOME terminal, the standard ways of moving forward or backward by one word do not work.

In spite of what the documentation says:

alt+b : Goes back one word at a time.

alt+f : Moves forward one word at a time.

If I do the above, I just open the drop-down menu for Tabs and Edit. How can I fix this?

just press ctrl-→ and ctrl-←

In the Terminal, go to Edit → Keyboard Shortcuts... and untick the Enable menu access keys box.

From the readline manpage (readline is the library that implements these commands):

An emacs-style notation is used to denote keystrokes. Control keys denoted by C-key, e.g., C-n means Control-N. Similarly, meta keys are denoted by M-key, so M-x means Meta-X. (On keyboards without a meta key, M-x means ESC x, i.e., press the Escape key then the x key. This makes ESC the meta prefix. The combination M-C-x means ESC-Control-x, or press the Escape key then hold the Control key while pressing the x key.)

@Galgalesh is correct that you use the Ctrl+arrow keys to jump words in Ubuntu. In many (most?) other distributions the key combo is Alt+arrows.

In order to use Alt+f/Alt+b without interfering with the menus, use Esc, f (press Esc, THEN press f, not both at the same time).

The reason I mention this is that you can use the Esc then (key) trick for other commands, too. E.g., if you've started editing a previous command and decide you want to revert it, use Esc, r.