It varies by make. For example:
Old Fiats, to leave just the side lights on for parking, press an interlock pin and turn the ignition key back one place before removing key.
Newer Fiats, switch the light switch off and on again with the ignition switch off.
My Renault: on the light switch, select sidelights rather than AUTO (there is no OFF position on the light switch, if you want lights off you leave in AUTO and switch off the ignition!).
My Fiesta was much the same, leave in AUTO all the time, switch to parking lights if want to leave on (though I think that did have an OFF position too).
nib