I have a ribbon cable that is not labeled and does not have a notch to prevent it from being installed backwards. How can I identify which pin is #1 on the connector?
Pin 1 on a ribbon cable (the cable itself, not the terminators) is usually colored differently than the other pins - often red.
See which edge of the cable (the cable, not the connector) is painted.
Usually flat cable has one of it strand with a colored strips (usually red). So pin #1 will be on that side. if the pins are not lined up in the connector it will be the one the furthest to the side.
Im not sure why sangretus response is doing so well. According to your post the ribbon is not marked. Additionally, the cable is just a wire so "wire #1" is arbitrary.
On the motherboard side osij2is is correct, they should have a #1 printed next to the terminal. On the other side your hardware user manual should help you determine where pin #1 is.
You could use a multimeter to identify it, and the label/mark it for future use.