You can attach a PC keyboard and mouse to an Android device, using Bluetooth or USB [2], and Android supports them surprisingly well.

Input methods that displays nothing on the screen

When you're using a physical keyboard, you don't need the soft keyboard to pop up and take valuable screen real-estate. You switch to one of these IMEs while using your hardware keyboard, and switch back when you want to use the soft keyboard again.

Once you have the new IME installed, here's how to select it.

PC keyboard equivalents to Android hard keys

Back Esc
Home Alt+Esc
Windows+Esc
Menu Context Menu key
Ctrl+Esc
Search hold Context Menu key
Windows+Space
Quick Launch [2] Windows key + <letter>
Volume multimedia keys

Additional shortcuts:

The above lists only things specific to PC keyboards. Androids with a sliding keyboard already support a large number of native shortcuts, see there for more. (even if your phone doesn't have a sliding keyboard, Android OS still supports those key shortcuts)

PC mouse equivalents to Android keys

screen tap Left click
Back Right click
Left side button
Home Middle click

apps that support PC keyboard keys

Most apps aren't designed to handle Ctrl/Alt/Esc/Fn keys. But there are a few that have improved support for them:

Android version

Note: The above shortcuts may differ by Android version. My phone is Android v4.1.1, Samsung GS3. Other lists I've seen [1] [2] didn't work very well on my phone.