The Canon S1iS lacks a hotshoe, the adapter that would let you mount an external flash to the camera.
You can still use an external flash with the S1. The solution is to use a "slave" flash. This is a regular flash unit with a light sensor attached. When you use the flash on the S1, the bright light is noticed by the sensor, and sets off the external flash.
There are two types of units: one is a flash with the sensor built in; the other is an sensor that is added to regular flashes. There's an article with more details at Slave Flash Photography.