Positive reinforcement is the best way to get across a message. I have two cats, and I've trained them both to be loving non-violent creatures through positive reinforcement. I expect to use a modified technique on children someday.
For positive reinforcement to work, the being has to know you don't want to harm it. The best way is by giving it some affection... in animals that are used to liking humans, a good back scratch or head rub will get the point across. In abused animals, this often involved a lot of repeitive crouching and staying still, or holding the animal calmly in a comfortable position while caressing it. It can take many months before an abused cat or dog to begin trusting humans again, but as long as you don't harm him/her, he/she will begin you, if not all humans again
For cats, my favored technique is to pick them up and hold them while pacing. Abused cats will resist violently, its important to not overreact when they do. Hold them as long as possible, and let them down gently when its too much. They will scratch and resist, but the longer you resist and remain calm, the quicker they will stop. It's okay to wear layers of clothing during this training process; it's most improtant that you do not react violently when the cat "defends" itself from your "love". It's hard to react calmly when you're bleeding profusely, and training a cat to not use his/her claws must come later.
If you're in too much pain from the resistance, put them down slowly. Cats usually upright themselves when falling, but they'll trust you more if they don't have to. Once they begin to trust you enough to hold them for a minute or more without resistance, you can begin diciplining them properly. This is when where they realize you might have a point, and they should pay attention.
Cats (and to a lesser extent dogs) will not listen until they trust you, so you must become better than the cat and not stoop to his/her level. Many cats do not trust humans and will overreact when humans are around... it's the owners responsibility to prove to this animal that such an overreaction is never necessary.
For smaller dogs, its the same technique but doesn't usually take as long as with a cat. For larger dogs, the whole "lifting and loving" technique can become quicklly impossible. Chasing and cornering an animal creates docility only in greatly inferior animals; if they think they can kill you, they just might try. Your job with bigger, violent (usually abused) dogs is to prove killing you has no benefit. Larger dogs require more of a martial arts-style training than an alpha-male-dominance relationship. It requires more dicipline and focus, more cooperative work and less defiant work. An inferior animal being tackled with a back-scratch might just not resist ("i cant win and this doesn't hurt now"); an equal animal will always resist ("I can win and this might hurt soon"), and a superior animal will always win ("I can win and I don't want this to hurt ever"). Humans don't often offer 6ft+ lions a belly rub, (thankfully, but also making this effect
harder to measure.)