Low Poly Water

This answer is far too late, but for others searching I just did this script as I was searching to do the same thing. put it on a plane (or for a much better lowpoly/faceted look, make a plane in a 3D modelling software, and in the unity import settings set Normals and Tangents to calculate and smoothing angle to 0. Then put my script on, you will have to play around allot with the range and speed, note that the range only is taken into effect in void start, so changing them in play mode will change nothing.

 using UnityEngine;
 using System.Collections;
 
 public class FacetedWater : MonoBehaviour {
     public Vector2 range = new Vector2(0.1f, 1);
     public float speed = 1;
     float[] randomTimes;
     Mesh mesh;
     
     void Start(){
         mesh = GetComponent<MeshFilter>().mesh;
         int i = 0;
         randomTimes = new float[mesh.vertices.Length];
         
         while (i < mesh.vertices.Length) {
             randomTimes[i] = Random.Range(range.x, range.y);
             
             i++;
         }
         
     }
     
     void Update() {
         mesh = GetComponent<MeshFilter>().mesh;
         Vector3[] vertices = mesh.vertices;
         Vector3[] normals = mesh.normals;
         int i = 0;
         while (i < vertices.Length) {
             vertices[i].y = 1 * Mathf.PingPong(Time.time*speed, randomTimes[i]);
             i++;
         }
         mesh.vertices = vertices;
     }
 }

Hope it can help someone

You can dynamically change the mesh by script using mesh class.

http://docs.unity3d.com/Manual/GeneratingMeshGeometryProcedurally.html

You're right - you simply need a function that displaces the vertices of a plane in a sinusoidal function with a bit of noise. But don't expect it to look quite like the above - Timothy Reynolds' is a master and his images are all about lighting!

If you're not familiar with coding, I suggest you look on the asset store. There's plenty of low cost (and perhaps even free) water scripts/shaders that do this.

https://www.assetstore.unity3d.com/en/#!/content/5141 I think there's a crumple mesh modifier here that can simulate water quite well.