The school ma’am in me wonders whether it would be wise for you to be wiring up a 500VA mains transformer if you’re not familiar with this. It doesn’t happen all that often, but people (and more distressingly, though even less often) their loved ones can go dead if the earth wiring and overcurrent protection (fuses to you and me) isn’t done right.
However, for what it’s worth, there seem to be four diodes on each side of the power supply which indicate that it’s a bridge rectifier (most solid-state ones are) in which case it doesn’t need a ground from the transformer. 18V AC connects to two nodes of the bridge and full-wave rectified ‘DC’ comes out of the other two nodes (plus and minus). You then connect this to a reservoir capacitor (sometimes, not strictly correctly, called a smoothing capacitor). Since you have two power supply channels and two windings on the transformer you might choose to keep them separate, using one winding for one channel and the other for the other.