KeyEvent: Each key press is described by a sequence of key events, Key events are generally accompanied by a key code.

KeyCode: is a constant that define the event, and is defined inside KeyEvent Class.

For example if you want to detect the KeyEvent "ENTER" :

 @Override
  public boolean onKeyDown( int keyCode, KeyEvent event ) {
    if( keyCode == KeyEvent.KEYCODE_ENTER) {
      //Do something...
      return true; 
    }
    return super.onKeyDown( keyCode, event );
  }

Answer to this question should be twofold. It is determined by the way how the key was generated. If it was press on the hardware key, then both approaches described below are valid. If it was press on the software key, then it depends on actual context.

1.) If key was result of the pressing on the soft keyboard that was obtained by long press on the Menu key:

You need to carefully override the following function:

@Override 
public boolean onKeyDown(int keyCode, KeyEvent event) {

    switch (keyCode) {
        case KeyEvent.KEYCODE_A:
        {
            //your Action code
            return true;
        }
    }
    return super.onKeyDown(keyCode, event);
}

2.) If your activity contains EditText, and softkeyboard was obtained from it, then first approach does not work because key event was already consumed by EditText. You need to use text changed Listener:

mMyEditText.addTextChangedListener(new TextWatcher()
{
    public void afterTextChanged(Editable s) 
    {
    }
    public void beforeTextChanged(CharSequence s, int start, int count, int after) 
    {
        /*This method is called to notify you that, within s, the count characters beginning at start are about to be replaced by new text with length after. It is an error to attempt to make changes to s from this callback.*/ 
    }
    public void onTextChanged(CharSequence s, int start, int before, int count) 
    {
    }
);

The answer was actually a little complicated, but not too bad, once I had some better feedback from other developers. See the explanation here, but for those that don't want to leave the page, basically do this:

import java.lang.Process;
import java.lang.Runtime;

// your code here
String keyPower = "input keyevent " + KeyEvent.KEYCODE_POWER;
Runtime runtime = Runtime.getRuntime();
Process proc = runtime.exec(keyPower);

Simplistic, but it gets it done, no matter what activity is being focused.

Here are some precision to Roman answer

BaseInputConnection  mInputConnection = new BaseInputConnection( findViewById(R.id.main_content), true);
KeyEvent kd = new KeyEvent(KeyEvent.ACTION_DOWN, KeyEvent.KEYCODE_MENU);
KeyEvent ku = new KeyEvent(KeyEvent.ACTION_UP, KeyEvent.KEYCODE_MENU);
mInputConnection.sendKeyEvent(kd);
mInputConnection.sendKeyEvent(ku);