Slide switches are usually wired by connecting to the centre pin and one of the outer pins. It doesn't matter which. For your circuit, you'll need a break in one of the wires between the LED and the power source. Again, it doesn't matter which. Connect one side of the break to the centre pin of the switch and the other side of the break to one of the outer pins.
There are three pins because in each position, the slide connects the centre pin to one of the outer pins, and disconnects it from the other. For your project you're only interested in making and breaking (switching on and off) one connection; so you only need to use one of the outer pins.
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