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On the inside of the door, in front of the window, and inside of where the mirror is mounted, there will be a plastic trim panel (probably contains the mirror adjustment lever).
Carefully pull off the mirror adjustment lever, and then carefully prise off the trim panel.
The bolts that attach the mirror to the door will be exposed. Unbolt the old mirror, and refit the new one.
Most cars have three bolts, but most cars also have a triangular plastic trim on the outside as part of the mirror assembly, which the 2002 Punto does not, and most cars have completely different housings for left and right mirrors, whereas the Punto uses the same housing for both sides, so there may be two bolts, or perhaps four smaller screws (I've replaced quite a few mirrors, but never on a Punto).