How can one get the coordinates of a particular point on a map in OpenLayers?
Handle click event on map Click handler. Here is one of many sample codes you can find in OpenLayers mailing list archives:
map.events.register('click', map, handleMapClick);
function handleMapClick(e)
{
var lonlat = map.getLonLatFromViewPortPx(e.xy);
// use lonlat
// If you are using OpenStreetMap (etc) tiles and want to convert back
// to gps coords add the following line :-
// lonlat.transform( map.projection,map.displayProjection);
// Longitude = lonlat.lon
// Latitude = lonlat.lat
}