As an example of the above method, let's say we number cards from lowest to highest then by suit alphabetically (so we'd go 2 Clubs, 2 Diamonds, 2 Hearts, 2 Spades, 3 Clubs, ... A Hearts, A Spades). Number the three cards (one is set aside, and one is the suit card) 1, 2, 3 from lowest to highest. Then for simplicity, we'll say S, 1, 2, 3 is lowest (add 1), then S, 1, 3, 2 (add 2), then S, 2, 1, 3 (add 3), then S, 2, 3, 1 (add 4), then S, 3, 1, 2 (add 5), and finally S, 3, 2, 1 (add 6).
So now I've made an actually complete method. Here's an example in action. I'm given H2, S8, CK, H8, C3. I have 2 Hearts and 2 Clubs, but I'm going to go with Hearts for my suit (semi-arbitrarily). H8 is six more than H2, so that's the one I set aside. H2 is my suit card. I want to indicate add 6, so I need the 'largest' permuation, 3, 2, 1. That happens to be CK, then S8, then C3. So I lay out for my partner: H2, CK, S8, C3.
My partner sees this and the H2 immediately tells him the hidden card is a Heart, from 3-8. He looks at the permuation of other cards and sees it's in decreasing order. He knows to add 6, so he announces the hidden card is H8 and is correct.
Phew. I'm more convinced of my method's correctness now.
PPE: Titan just confirmed it's correct, but still here's an example.