Finally, some life in the Judo/Jujutsu section
Ok, an Osoto Gari is the standard big outer reap, what some people will call a sweep. In judo, the difference between a reap and a sweep is that there is no weight on the foot that you sweep, and there is on the one you reap. The "classic" Osoto Gari is where you will break your opponents balance to their back right corner, shifting the majority of their weight onto their right heel. This can be done using a left foot forward tsugi ashi in conjunction with the hands, grabbing the lapel and sleeve or arm and neck, to shift uke's weight. Once you've got their balance broken your left foot should be about the same depth as their right, the one you are going to reap. From there bring your right leg up past their right leg and sweep back, making thigh to thigh contact, and remember to follow through. Don't stop when you feel contact, continue with the reap, which will bend your upper body slightly forward, and if you move your hands with your body, will cause uke to shift their weight even more to that corner, which really augments the power of the throw.
The problem with the "classic" O Soto Gari, is everybody can see it coming from a mile away and hold you out or shift their leg to regain their balance....