In most cases, your glass comes ready to hang with a chain or cord attached. If you want to hang your piece in a window, I recommend using a sturdy hook that’s screwed into the window frame or the window lock/latch if yours has one.
I’m not a fan of using suction cups to hang your piece in a window, especially for heavier pieces, since they can detach over time and cause your piece to fall. For wall hanging, a nail works for smaller pieces, but using a stud for large/framed pieces is most secure.