Due in some part to Mike Sigman's probing questions, I have been investigating this area for some time. I'll try to list some of the things I've found that seem to be making a difference in physical technique. Please understand that nothing I write here is being presented as final answers in any way. This is simply my attempt at answering your question by presenting my own investigations on kokyu / ki / aiki in three traditions I have had some access to: Yoshinkan Aikido / Abe Sensei / Daito ryu. I am still continuing to research this, and coincidentally, Inoue Sensei of the Yoshinkan will be here this weekend in Phila. I believe a major topic in the private sessions will be kokyu. An important part of this is that he has written a book in Japanese about kokyu, and he has spoken in the past about the specific differences in Aikido and Daito ryu in relation to kokyu, ki, and aiki.
The books of Gozo Shioda talk about the different powers that make up aikido, and Kokyu and Ki are dealt with specifically. The power of the centerline, the power of breath, the power of focus are all spoken of as combining to be the power of ki, a mastery of balance (or as Mike says, balancing all of these powers). I'm not going to go into much depth on this now...your best option is to read his books (esp. his autobiography, Mastering Aikido, the basic course, and the third one whose title I forget just now). One of the key features of reading Shioda Kancho's works has been his statement that the basic training in aikido yoshinkan is meant to develop this kokyu power. You also get clues from statements like the power comes from the big toe.
Combined with this are statements from Chida Sensei, one of the top shihan in Yoshinkan, who has made statements about 'taking the slack out of' the relationship between shite and uke. In other words, there needs to be a certain amount of relaxed (?) tension between shite and uke so that their centers are connected so that when you move, uke must move if the connection is maintained.
I have also had input from other practitioners in the yoshinkan, specifically Tom Yawata. Tom's experience with a Daito ryu group has been beneficial as well. You can see his contributions for yourself at http://www.aikidojournal.com/?id=1045
In the thread mentioned above and other sources, Daito ryu does not seem to use the phrase 'kokyu'. That seems to be unique to Aikido. The focus in Daito ryu is on 'aiki' more so than ki. This is an interesting area for investigation, as in viewing films of Daito ryu adepts, Ueshiba, and Gozo Shioda, there seems to be some strong commonalities. If you look at a technique such as shihonage and the use of 'aiki' in locking uke's elbows and raising them, you also see similarities to what I saw with Abe Sensei's use of kokyu / ki.
Due to the kindness of Shaun Ravens, I was able to spend 3 days training in Iowa with Abe Sensei, who focused on using ki in technique during his time there. Most of the techniques we studied involved focusing on bringing the power from the ground using the big toe, 'clamping down' on the 'one point' with the breath, keeping our arms straight and uke's arms straight. Abe Sensei's methods seemed to me to work best with absolutely no slack in the relationship between shite and uke, at least while learning his methods. Perhaps the need for this is greatly reduced as you advance.
Some of My Own Observations
From all of the above.
Relax the shoulders as much as possible. The kokyu / ki / Aiki power seems to get stopped in shoulders if there is any tension there at all.
Close the spine. There was a marked difference in my sucsess at Abe Sensei's technique when I relaxed the shoulders in combination with closing the gap between the shoulder blades. This helped not only with Abe Sensei's technique, but with Yoshinkan waza as well.
Focus on the big toe...that's where the power seems to come from. Keep your weight centered on the ball of the foot beneath the big toe, and try to structurally align everything between there and your contact with uke.
Don't worry about 'setting up uke' at first by having them attack in a specific way. It seems that at first this gets you feeling what it takes to move in the correct direction. Applying these (and other) methods in more adverse circumstances seems to come much later.