OK, handle the WM_SIZE message. The width/height of client area are passed in the lParam.
After that call MoveWindow on your button.
clientWidth = LOWORD(lParam); // width of client area
clientHeight = HIWORD(lParam); // height of client area
Hope that helps.
// buttonWidth, buttonHeight previously declared.
MoveWindow( hWndButton, /*handle to button*/
30, /*pixels from left side of window*/
clientHeight - buttonHeight - 30, /* distance from bottom*/
1, /*tell it to redraw the window*/ );