Get coordinates of mouse-click on plane

I’m basically a newbie with Unity. I’ve created some simple projects from tutorials but only have basic understanding.
I have a plane in 3D space. I want to click on the plane with the mouse and get the coordinates for that click (i.e. whereabouts on the plane I clicked) .
Currently I can only get the world coordinates on-click. I tried getting the position of the plane in world space so that I can convert my mouse click coordinates to plane coordinates but this doesn’t do what I expected and actually gives me the coordinates on plane relative to the transform associate with my player script. I feel like there may be a better way to do this anyway.

Here is my simplified PlayerMovement script:

public class PlayerMovement : MonoBehaviour {

// Use this for initialization
void Start () {
	plane = GetComponent(typeof(MeshFilter)) as MeshFilter;
}

void Update() {
	if (Input.GetMouseButtonDown (0)) {
		Debug.Log ("mouseDown = " + Input.mousePosition.x + " " + Input.mousePosition.y);
		Debug.Log ("position in plane = " + plane.transform.position);
	}
}

}

I’d really appreciate any pointers here.
I imagine it’s simple enough when you know how. I have looked at quite a few articles and pieces of documentation but I just can’t find a solution.
Thanks in advance.

You can try this:

    private void Update()
    {
        if (Input.GetMouseButtonDown(0))
        {
            clicked();
        }
    }

    void Clicked()
    {
        var ray = Camera.main.ScreenPointToRay(Input.mousePosition);

        RaycastHit hit = new RaycastHit();

        if (Physics.Raycast (ray, out hit))
        {
            Debug.Log(hit.collider.gameObject.name);
        }
    }

let me know if you have questions.