O-goshi is considered the basic hip throw. I would imagine that this technique was derived from Uki-goshi, as the Ju-Jitsu hip technique uses less hip than we do in Judo.
To perform the technique, from a standard grip (right handed), let go of the collar and put your arm around your opponents back - turning so that your back is towards them. Most instructors demonstrate bending your knees to get lower than your opponent - but you can do this technique without this if you use enough hip.
When in position, rotate your hips in a large clockwise circle, akin to using a hula-hoop, lifting your partner with the initial contact, and then removing your partners support by continuing the circle and taking away your hips.