In the API docs, there are a couple of simple examples of adding a polygon to a map. Here's the initialize() function from the simple Bermuda Triangle example with the addition of adding an event listener to remove the polygon when clicked.
function initialize() {
var myLatLng = new google.maps.LatLng(24.886436490787712, -70.2685546875);
var myOptions = {
zoom: 5,
center: myLatLng,
mapTypeId: google.maps.MapTypeId.TERRAIN
};
var bermudaTriangle;
var map = new google.maps.Map(document.getElementById("map_canvas"),
myOptions);
var triangleCoords = [
new google.maps.LatLng(25.774252, -80.190262),
new google.maps.LatLng(18.466465, -66.118292),
new google.maps.LatLng(32.321384, -64.75737),
new google.maps.LatLng(25.774252, -80.190262)
];
// Construct the polygon
bermudaTriangle = new google.maps.Polygon({
paths: triangleCoords,
strokeColor: "#FF0000",
strokeOpacity: 0.8,
strokeWeight: 2,
fillColor: "#FF0000",
fillOpacity: 0.35
});
bermudaTriangle.setMap(map);
// add an event listener
google.maps.event.addListener(bermudaTriangle, 'click', function() {
this.setMap(null);
});
}