Find forcing candidates
White should scan checks before quiet attacks. Nd6+ attacks the king on e8 and queen on c8 at the same time. Because the move gives check, Black cannot simply move the queen.
Verify the reply
After the king responds, the knight remains able to capture the queen. The value of the fork comes from move order: the royal target forces the first response.
Generalise the pattern
Knight forks are easiest to notice when you map the knight's destination squares around valuable targets. Checks, attacks on queens, and attacks on loose rooks deserve immediate calculation.