TL;DR: if quickdraw gate faces the same way as the clipping arm, use method 1, otherwise use method 2 from this video.
In the first approximation, in lead climbing, there are 4 possible clipping scenarios:
| Quickdraw faces right → | Quickdraw faces left ← | |
|---|---|---|
| Clipping with the right arm (R) | R→ | R← |
| Clipping with the left arm (L) | L→ | L← |
There can be more efficient ways of clipping depending on the quickdraw position relative to the climber (left or right, high or low). Ignoring them allows reducing the number of scenarios to just 4.
Since right-arm and left-arm techniques are mirror images of each other, we need to learn only these 2 methods:
Quickdraw faces the same side as the clipping arm: R→ or L←
Clamp the rope with fingers 4+5, balance it over fingers 2+3, control the quickdraw with the thumb and fingers 2+3, push the rope in.
Quickdraw faces the other side as the clipping arm: R← or L→
Take the rope in the same way, invert the rope (flip the palm), pinch the rope with thumb and finger 2, stabilize quickdraw with the middle finger, push the rope in.
Videos: