I can assure you, the keyboard is much, much faster for most things.
In Office (and most word processors), for example, people will be clicking the bold and italic buttons. When using Office, you're typing, with your hands on the keyboard. Keep them there:
* Control+ toggles bold
* Control+u toggles underline
* Control+i toggles italics
When using Windows, you (probably) have a Start key (Windows logo button) then opens the Start menu (this is actually the same as Control+esc). Use it. It's also often faster to then use arrow keys and letters to traverse the menu. For common programs, edit the shortcut properties and set shortcut keys, so Control+Alt+something will open your web browser and Control+Alt+something_else opens your email client.
If you're jumping position from one side of the screen to the other, using the mouse can be nice, but when it's nearby, the keyboard can get you there faster. Tab is a good key. Use it. Press tab to jump to the next form field or button (or link). Use home and end to get to the end or beginning of the line, or Control+home/end to get to the beginning/end of the file. Control+left/right will jump an entire word.
Now for the big three:
Top copy selected text or files to clipboard, use Control+c. To paste, Shift+Insert or Control+v. (To cut, Control+x). And to switch between multiple windows, use alt+tab and alt+shift+tab. It will be in order of most recently selected programs.
