Tani-Otoshi is a basic Judo counter throw. (It recently became my favorite throw when I used it to beat someone from Eton in a match.)
It is generally used to counter rotational throwing techniques and is fairly ineffective against most leg sweeps.
To do Tani-Otoshi you should take a standard grip (your right hand on your opponent’s left lapel and your left hand on his/her right sleeve. {If you are of a sinister persuasion then this throw will only really work if you are fight another left-hander in which case swap the above around.}) Your Opponent will turn in for an attack thereby attempting top line his/her hips up with yours. This will cause his/her torso to end up in the crook of your right arm. When this happens you need to move fast: don’t lose your grip but step to your right but keep your left heel roughly where it is. Then sit down and pull your opponent down over your outstretched left leg.
This throw uses your opponent’s momentum to move him/her over your leg but you should uses your arms to make sure he/she doesn’t land on your knee.
This is an excellent throw especially if it is done unexpectedly but one problem is that it doesn’t allow you to follow down into a hold as naturally as some throws do. So if you do it but don’t score ten points (thus ending the contest) your opponent has more time to get off his/her back.