Using a plastic opening tool (or similar) in one hand, push down one pin holding the heat sink on the logic board. The spring under the pin will provide moderate resistance.

While holding the pin down from the heat sink side of the board, use a pair of pliers in your other hand on the underside of the board to squeeze both barbs against the plastic shaft of the pin.

With both barbs squeezed together, push the pin through its hole in the logic board.

Repeat this process for each of the four pins holding the heat sink on the logic board.