The secret is simple, you need to:
- place the master link (the part with the pins) with the opening towards you,
- bend (flex) the chain so the open ends of the pins come closer to each other,
- put the flat part of the master link,
- release the bend allowing the pins to snap into the flat part of the master link.
Since one picture saves 1000 words, they say...
The bend of the chain is a bit exaggerated, only to show the idea of the action required. One bends the chain using their hands.
And from my own experience - I prefer this type of master link over power link since linking and breaking the chain does not require literally any tools (excepto for one's hands) making it great for road-side repairs. Disengaging power link does require at least pliers (dedicated tool recommended) unless one has enormous strength at their fingertips.