The simplest way to click on 3D objects in Panda3D is to use very simplistic collision detection coupled with event processing.

First, after a CollisonTraverser and a CollisionHandler have been setup, attach a CollisionRay node to the camera. This node will have its set_from_collide_mask() set to GeomNode::get_default_collide_mask() in order to be as general as possible.

PT(MouseWatcher) mouseWatcher;
PT(CollisionRay) pickerRay;
CollisionTraverser myTraverser = CollisionTraverser("ctraverser");
PT(CollisionHandlerQueue) myHandler;
PT(CollisionNode) pickerNode;
NodePath pickerNP;
 
pickerNode = new CollisionNode("mouseRay");
pickerNP = camera.attach_new_node (pickerNode);
pickerNode->set_from_collide_mask(GeomNode::get_default_collide_mask());
pickerRay = new CollisionRay();
pickerNode->add_solid(pickerRay);
myHandler = new CollisionHandlerQueue();
myTraverser.add_collider(pickerNP, myHandler);

For any object that you want to be pickable you should add a flag to it. The easiest way is to use the set_tag() function:

object1.set_tag("myObjectTag", "1");
object2.set_tag("myObjectTag", "2");

The above example sets the tag 'myObjectTag' on two objects in your graph that you want to designate as pickable. We will check for the presence of this tag after we get the response back from the collision system.

Now assume that the function my_function() is set up to be called for the 'mouse1' event. In my_function() is where you call picker_ray.set_from_lens(origin, destX, destY). This makes the ray's origin origin and the ray's vector the direction from origin to the point (destX, destY).

void myFunction(){
   if (!mouseWatcher->has_mouse()){
      // The mouse is probably outside the screen.
      return;
   }
   // This gives up the screen coordinates of the mouse.
   LPoint2f mpos = mouseWatcher->get_mouse();
 
   // This makes the ray's origin the camera and makes the ray point 
   // to the screen coordinates of the mouse.
   pickerRay->set_from_lens(window->get_camera(0), mpos.get_x(), mpos.get_y());
}

After this, you now call the traverser like any other collision, get the closest object and "pick" it.

The node returned by the collision system may not be the object itself, but might be just a part of the object. In particular, it will be one of the GeomNodes that make up the object. (The GeomNode class contains the visible geometry primitives that are used to define renderable objects in Panda3D.) Since your object might consist of more than one GeomNode, what you probably would prefer to get is the NodePath that represents the parent of all of these GeomNodes; that is, the NodePath that you set the 'myObjectTag' tag on above.

You can use node_path.find_net_tag() to return the parent NodePath that contains a specified tag.

(There are also other, similar methods on NodePath that can be used to query the tag specified on a parent node, such as get_net_tag() and has_net_tag(). For simplicity, we shall restrict this example to find_net_tag().)