As far as I remember, you just spool it out. The cable is tucked into a hole in the drum; just pull it out of the hole when you get to the end.
BUT, if you want to use synthetic cable, you'll want to polish up the winch drum and drum sides to remove any burrs that might have been created from the steel rope. The burrs will slice your synthetic fibres. Also replace your fairlead with a new one for the same reason, and ensure that the new one is compatible with synthetic (something to do with the placement of the rollers and the synthetic rope getting stuck). And again, for the same reason, you will want to replace your snatch block or at least the pulley.
Since you're in Edmonton, I assume you'll be dragging it through all kinds of mud. Make sure you clean your synthetic cable regularly; muddy water will evaporate leaving the silica in the rope, which will slice the synthetic fibres from the inside and you won't even see the damage.
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