Super easy in Kentico. Once your web part is created, go to the "Widgets" module, add a new widget, and select your web part as it's base.
Then simply go to Properties, hide/set/show whatever properties you want the user to use, then make sure the widget is added to the site, and lastly go to Security tab and hit allow it to be used by whatever you want (i usually do authenticated users). Now it will show!