It sounds like you have a traditional headset, the type with two rings of ball bearings in an open form (called retainers), rather than in cartridges. There are two common types of retainers, and how to orient them depends which type you have. In lieu of a photo, go by this:
If the ring is on the inside, like this one
, with fingers reaching outwards to hold the balls, put the ring facing inwards towards the frame.
If the ring is on the outside, like this one
, with fingers reaching inwards
to hold the balls, put the ring facing outwards from the frame.
The idea is that the ring shouldn't get in the way as load is transferred from the bearing cone through the balls to the bearing cup. Simple enough, right?
At the top, the split ring acts like a collet to keep the fork centered in the upper bearing cone. So it'll have its bevelled side facing downwards into a matching part of the upper bearing cone.