Just to add from the perspective of a jitsuka rather than a judoka, tani-otoshi (valley drop) is a particularly nasty throw to fall from because you invariably end up landing on your shoulder blades and the back of your head hits the mat the first few times you try.
Essentially, what happens is a step behind both of the attacker's legs, followed by pushing the attacker over.
From a right handed punch by uke (attacker), uke should have stepped forward with their right foot, leaving them in a line facing tori (defender).
Tori blocks the oncoming punch (usually with the right hand) as they step forward with the left leg, placing it behind uke.
Tori then drops their weight and bends their knees, bringing their thigh to (ideally) just below the level of uke's knees.
Tori then brings their left arm up, places it in uke's chest / neck and pushes back, causing uke to fall backwards over tori's leg. If uke is a big person or is being difficult then tori's right arm can be used to pick up uke's leg as well (making the fall even harder).
In situations where tori knows how uke will be punching eg. the sensei has shouted out 'Punch right then left', the initial block can be forgotten to speed up the throw. Trying this is not a good idea unless you are DEFINITELY sure which side uke will punch with, otherwise you will eventually get punched in the face. There are also variations where the initial block is done with the left arm which allows a smoother and quicker transition to the actul throw.