I spend a fair amount of time looking over people's shoulders while instructing them on how to do various things on their computers. Of all the ways in which many people could improve their productivity, I think learning basic hotkeys would probably lead to the most noticeable results. That's why I'm going to go over some of the most common tasks that you can complete using your keyboard instead of your mouse.
These only apply to computers running Windows. They may very well work with Macs or Linux, but I wouldn't really know about all that.
To be clear about the shorthand, the plus (+) symbol means that you hit multiple keys at the same time. For example, "ctrl+s" means that you hit the ctrl and s keys at the same time. The ctrl, shift and alt buttons can be pressed and held before other keys so with "ctrl+s" you can hit and hold ctrl before hitting the "s" button if you want.
- copy (ctrl+c) - If you have something selected (text, an image, a file or folder, etc), this will copy the item to your clipboard so you can paste it later.
- cut (ctrl+x) - This is like copy but it deletes the selected text in addition to copying it. Use this if you want to move the content rather than duplicate it
- paste (ctrl+v) - Use this to insert whatever you previously copied to the clipboard into whatever program has the focus.
- show desktop (windows+d) - This minimizes all your windows so that you can see the desktop quickly.
- lock computer (windows+l) - You may be expected to lock your computer at work. Rather than doing it the normal way (ctrl+alt+delete), just use this hotkey combo.
- switch windows (alt-tab) - This rotates through the open applications on your computer.
- switch windows reverse (alt+tab+shift) - The shift key generally reverses the direction of a hotkey command. In this case, you rotate through windows backwards.
- open explorer (windows+e) - This just opens a basic file browser (rather than going to "My Computer" in the start menu).
Common Application Shorcuts
- new tab (ctrl+t) - In any application that supports tabs (like most web browsers), you can open a new tab with this command.
- switch tabs (ctrl+tab) - This works just like rotating through windows, but it instead rotates through open tabs within the application.
- switch tabs backwards (ctrl+shift+tab) - Once again, holding shift reverses the direction of the operation.
- search (ctrl+f) - Most applications have some way to search for text. This brings up the text box that lets you type in the search terms.
- save (ctrl+s) - Save the current document, web page, etc.
- refresh (ctrl+r or f5) - If you want to refresh a web page, use either of these two hotkey combos.
- close (ctrl+w) - Generally, tabs or whole applications can be closed with this command. Try opening a new tab, and then closing it with ctrl+w.
- undo (ctrl+z) - If you make an edit that you don't like, this reverts back to before the edit was made.
- redo (ctrl+y or ctrl+shift+z) - This command helps you if you undo something but then decide that you want it back. Most programs use ctrl+y, but some use ctrl+shift+z.
- select all (ctrl+a) - This highlights all the content in the application.
- advance focus (tab) - When you're filling out a form online, you don't need to click on each field. Just hit tab to advance to the next field.
- rewind focus (shift+tab) - Once again, shift causes the command to rotate in the reverse order.
- Open in a new tab (middle mouse button) - Ok, this isn't actually a hotkey because it uses your mouse, but you should know it anyway. If you click on a link with your middle mouse button, it will open that link in a new tab so that you don't lose your place on the page you're looking at.
That's all the important ones that I can think of right now. I skipped some like printing because they aren't used often (by me at least) and text selection/navigation because that seems too complicated to explain here.
Let me know in the comments if I left out any of your favorites.