It's a case of pressure and release. Just like all other training. Put the leg on lightly, if you get no response, ask a little firmer, and if you get no response then go for the dressage whip and give a bit of a tap. *Usually* most horses will react to the tap if they're stubborn off the leg, and many of them will jump forward so be sure not to 'hit' them in the mouth when they do so. If the horse leaps forward and takes off, let it do so, and then bring it onto a circle and back to halt/walk (whatever pace you were at originally) and go through the process again. It doesn't matter that they leap the first couple of goes, because they are reacting positively by going forward to your forward aid and will soon figure out that they only need to go forward not launch themselves ;)
If you have yourself a horse who is painfully stubborn (I have only met ONE horse who I could absolutely NOT get forward, we tried everything with her, lungeing, lunge whips behind her, a good hard crack with the dressage whip on her backside, spooking for forwards with a plastic bag on the end of the whip etc. all as extreme measures and nothing other than having a horse in front of her, or someone shaking a bucket of food (haha!) would get her to go forward!!), then you can go for some more 'extreme' measures than a light leg and small tap.
One that I like is Jane Savoie's method. If the horse doesn't respond to the light leg, take both legs off for a moment, move them back slightly them apply them slightly behind the girth. Often that will wake the horse up and they'll go forward. It is the constant pressure on their sides that they deaden to, so if you're squeezing and squeezing with your legs and booting the hell out of the horse's sides, they're just going to brace and deaden to it. Where as taking the leg off completely gives them a moment of no pressure, and when the leg comes back on it 'shocks' them.
You can also try having someone in the middle of your circle with a lunge whip (if your horse know's how to lunge and isn't going to freak out at the whip). Ride a 20m circle around the person, and ask your horse for an upward transitions (i.e. Walk - trot). Ask as I first described (light leg, slight kick, tap with the dressage whip behind your leg) and if you don't get a reaction, have the person in the middle flick the lunge whip towards horse's hind quarters, and walk towards it's hindquarters if need be. This method doesn't usually take long if the horse is accustomed to lunging without a rider, and it will pick up quite quickly that reacting to the leg the first time means it won't get the lunge whip flicked at it.
The key is to remove all pressure the instant the horse reacts. I like to hold my reins at the buckle and hold onto the cantle of my saddle while doing these exercises with a green horse. Just makes sure you've got a stable, balanced and deep seat so you can stay on if they leap! You want the 'front door' to be totally open (loose reins), and the back door to be closed, as though they're an unwelcome guest in your house and your pushing the door shut behind them. So sit back a little, legs on etc. you want it all to come from behind.
If horse decides to be a little brat and back up or spin, keep maintain the pressure, don't touch to reins, don't move in the saddle etc. Just sit there, keep the pressure on and the second horse takes a step forward, release all pressure and allow horse to move off.