For me, the goal is to get the weight
off the front foot. This is accomplish-able in one of two ways: to attack or feign an attack.
Attacking requires less timing and risk but is hard to do against a good, mobile opponent. You want to attack (while slightly advancing, or threatening to advance) to get their weight on their back leg. A good way to do this (given that you are fighting an orthodox fighter) is to get slightly on the right of your opponent and throw a jab or hook. If your distance is good (far enough away where he can't easily hit you with a left of his own but close enough where he is worried), he will either lean back slightly to get out of the way or readjust to be more forward facing. That is when you take that extra small step and sweep his front foot out.
You can also try to just fire a quick, advancing rear or lead hand attack to get them to lean back, but if you're slow and flat footed like me, your opponent is probably gonna just back away instead of lean.
The other way is to feign an attack and get your opponent to push off his back foot to try and attack you.
In Karate competition, this is a fantastically effective move:
In full contact competitions, it's a lot harder to pull off because people aren't attacking off springs. You have to step slightly with your left and shift your weight to convince your opponent you are committed to an attack (but be far enough out that they have to step to land on you) and then step to the right with your read leg and scoop them on their ass.
And to be honest, might not be very possible. The closest thing I've ever seen to it being successful is Lyoto on BJ Penn: as Penn is attacking, Lyoto very quickly throws his hands forward and makes a very slight step forward. Penn reacts to this by ducking to the right and beginning to wind up his rear hand--- before Penn can even begin to shift his weight, Lyoto has him on his ass.
The difference, of course, is that Lyoto is in southpaw so he scoops from the outside and it is all in one motion--- no step to the right with your rear and bring your lead across. Still, it's the same method--- get the opponent to react so that his weight is off his front foot and sweep them off balance.
One or two more things that no one has said: Aim low. The lower the sweep, the less leverage he has. Think Bendo against Nate: The latter would lazily raise his front foot to check and Bendo occasionally would kick reallly low and it would sweep Nate on his ass.
The instep is a common area people use on their foot to sweep, but you can scoop more effectively if you turn your foot in and hit with the sole (although I've landed without turning my foot back down and hurt my foot like that).