It’s been a while since I did this, but IF memory serves me right, the white bit is a “M” shape, where the bottom of the two legs clip into the board and the two upper points attach to the key itself. Squeeze (gently!) the two legs together to get them into the brackets of the board, and then simply push the key straight down onto the pair of white “M"s until it clicks.
I’ve attached a dusty and slightly blurred pic from the Vaio SZ keyboard - it doesn’t have the metal bit covering the connectors so you can see it (kinda).
Click thumbnail to see full-size image