Copy and Modify selected text in different application

Your question has two answers

How can my app set a global hotkey

You have to call an API funcion called RegisterHotKey

BOOL RegisterHotKey(
    HWND hWnd,         // window to receive hot-key notification
    int id,            // identifier of hot key
    UINT fsModifiers,  // key-modifier flags
    UINT vk            // virtual-key code
);

More info here: http://www.codeproject.com/KB/system/nishhotkeys01.aspx

How to get the selected text from the foreground window

Easiest way is to send crl-C to the window and then capture the clipboard content.

[DllImport("User32.dll")] 
private static extern bool SetForegroundWindow(IntPtr hWnd);

[DllImport("user32.dll", CharSet=CharSet.Auto)]
static public extern IntPtr GetForegroundWindow();

[DllImport("user32.dll")]
static extern void keybd_event(byte bVk, byte bScan, uint dwFlags, uint dwExtraInfo);


.....

private void SendCtrlC(IntPtr hWnd)
    {
    uint KEYEVENTF_KEYUP = 2;
    byte VK_CONTROL = 0x11;
    SetForegroundWindow(hWnd);
    keybd_event(VK_CONTROL,0,0,0);
    keybd_event (0x43, 0, 0, 0 ); //Send the C key (43 is "C")
    keybd_event (0x43, 0, KEYEVENTF_KEYUP, 0);
    keybd_event (VK_CONTROL, 0, KEYEVENTF_KEYUP, 0);// 'Left Control Up

}

Disclaimer: Code by Marcus Peters from here: http://bytes.com/forum/post1029553-5.html
Posted here for your convenience.

Use the Clipboard class to copy the contents to the clipboard, then paste in the notepad.

You could also write the contents to a text file and open it with notepad by running the notepad.exe application with the text file's path as a command line parameter.

UPDATE 2020

How to get the selected text from the foreground window

No idea for how long has this been possible but instead of fighting with Win32 programming (mostly user32.dll and various Windows messages like WM_GETTEXT, WM_COPY and various SendMessage(handle, WM_GETTEXT, maxLength, sb) calls) which is advised in most of SO threads on this topic, I easily managed to access selected text in any window in my C# code followingly:

// programatically copy selected text into clipboard
await System.Threading.Tasks.Task.Factory.StartNew(fetchSelectionToClipboard);

// access clipboard which now contains selected text in foreground window (active application)
await System.Threading.Tasks.Task.Factory.StartNew(useClipBoardValue);

Here the methods being called:

static void fetchSelectionToClipboard()
{
  Thread.Sleep(400);
  SendKeys.SendWait("^c");   // magic line which copies selected text to clipboard
  Thread.Sleep(400);
}

// depends on the type of your app, you sometimes need to access clipboard from a Single Thread Appartment model..therefore I'm creating a new thread here
static void useClipBoardValue()
{
  Exception threadEx = null;
  // Single Thread Apartment model
  Thread staThread = new Thread(
     delegate ()
       {
          try
          {
             Console.WriteLine(Clipboard.GetText());
          }
          catch (Exception ex)
          {
            threadEx = ex;
          }
      });
  staThread.SetApartmentState(ApartmentState.STA);
  staThread.Start();
  staThread.Join();
}