You simply add the click event to the GraphicsLayer that you're adding your points.
var GLayer = new GraphicsLayer();
GLayer.on("click", runClickEvent);
function runClickEvent(evt){
}
There is another way to do this, in addition. When you construct the graphic, you can add an InfoTemplate (in 3.x) or PopupTemplate (in 4.x). See this sample that shows how to incorporate the attributes and PopupTemplate into a graphics that is added to a map (in this case, the line).