We don't have a spirit. We are a spirit, both before and after we die. The difference is that during the physical life cycle, we are a spirit with a body. After we die, the spirit that is us is free to move on, away from the body.

In the normal process of dying, the body becomes unable to produce enough energy to sustain itself and maintain a functioning brain. The body intelligence sends out a death signal, not unlike a signal from a radio beacon. When that signal is received, loved ones who have already passed on may come to greet you and accompany you on your journey, providing comfort by their presence.  Sometimes, a beam of light will guide you. There are other possibilities as well. However it happens, the experience of transition into the second phase of life is usually a joyous one.