The basic chain setup, for either stock breeds or basic English disciplines/breeds shown in a halter, is fairly simple. I'll break it down into short steps to try to keep it simple and clear.
Standing on the near side, thread the chain clip through the side ring near the muzzle (the ring that you would snap a crosstie to). You're bringing the clip in from the outside - think hitting the bullseye on the horse's face inside the ring.
Next, take the snap and run it either over or under the horse's nose. That's a judgement call on your part, whatever your horse is more comfortable with. I prefer under the jaw, personally. I know people who go over the nose because under the jaw upsets the horse and send him/her up.
Now, move to the off-side of the horse, and bring the clip out from inside of the corresponding "cross-tie" ring on that side. To review, as you're looking head-on at the horse, you should now have the chain coming in from the right, either down under the jaw or up over the nose, and out to the left.
Next, still on the off side, you're going to snap the clip to the upper side-ring of the halter to secure it. If your chain is still hanging more than 3 inches from the "starting point" on the near side, you're going to take up that slack on the off side by threading the clip through the upper ring (come out from inside). If you need to take the slack up this way, you'll need to secure the chain by clipping to it midway down its length
I hope these pics are helpful to you. Sorry about the size...
Focus on the front exhibitor (1043) - this is a good example of the over-nose configuration. Her halter could be slightly better fitted to the horse, but you can see how to run the chain.
This is the same team at a different show, with the under-jaw configuration. The near side looks the same as in the first picture, and you can see how she's looped the chain back over itself on the off side to take up the slack. Again, the halter needs to be adjusted smaller or swapped for a better fitting size. Additionally, the chain hangs too far on the near side - note how far her hand is from the gelding's muzzle. On the off side, the clip could probably be attached to the lower ring to get the shank to the proper length.
Disclaimer: My photos, but not of me or my horse. Please do not critique horse or exhibitor; photos are only to demonstrate the chain configuration. Thanks!