How to add Property Search or some other widget shortcode in Madison theme?

Just put shortcode to the content of your page or widget to some of your widget area.

The list of available shortcodes for WP-Property you can find here.

The list of available shortcodes for WP-Property add-ons you can find here.

WP-Property Widget you can find in Appearance/Widget tab and put them to any widget area you need. Available WP-Property Widgets are following: Property Overview, Property Terms, Property Meta, Featured Properties, Child Properties, Featured Properties, Latest Properties, Other Properties, Property Attributes, Property Search, Property Gallery. More info on WP-Property product page.

FYI, you can use Text widget in order to put shortcode into it.