As far as teaching Liberty, it is just a matter of refining your cues to the point that a halter and lead are unnecessary. Anything you want to teach at liberty, start in hand/on line and get your cues softer and softer until the rope is mostly draped to the ground and your horse is still responding to you.
Check out youtube there are lots of inspirational liberty videos, many don't contain the how to do, but there are many ideas of what to do. Honzaq Blaha's videos are totally awesome and inspirational, though not informative.
I have been a Parelli student for quite a while, it is the main influence for my training. I also really enjoy reading Ferdinand Hempfling, and Fredric Pignon when I want to refine my techniques. Fargo & Me, Liberty 1 - YouTube
That is a link to a short brag video I shot with my horse last year, so you can decide what my advice is worth. Liberty teaches you to more aware of your body language and attitude, than you may even be aware is possible! Don't completely shun the use of food rewards, but also don't become reliant on them. Pushing your horse too hard is the worst thing you can do if liberty is your goal, patience PATIENCE PATIENCE
, with a good sence of humor is what it takes to teach liberty. You will have miscomunications from time to time, staying relaxed and accepting what your horse is ready to offer will keep you progressing.