two players on a single screen

Do you want them to move at the same time with the same movements? If so; just simply add another sprite so you have your player 1, and your player 2, then add the same movement script.

If you want two players with different movement just copy the same script but change movement to maybe the arrow keys instead of W-A-S-D or oppsite? :)

Use the Input manager to set up separate axes for each player: e.g. "Horizontal1", "Vertical1", "Fire1", and "Horizontal2", "Vertical2", "Fire2". In the player input script attached to each player, reference the appropriate input. That's it.

 using UnityEngine;
 using System.Collections;
 
 //handles player movement, utilising the CharacterMotor class
 [RequireComponent(typeof(CharacterMotor))]
 [RequireComponent(typeof(DealDamage))]
 [RequireComponent(typeof(AudioSource))]
 public class PlayerMove : MonoBehaviour 
 {
     //setup
     public bool sidescroller;                    //if true, won't apply vertical input
     public Transform mainCam, floorChecks;        //main camera, and floorChecks object. FloorChecks are raycasted down from to check the player is grounded.
     public Animator animator;                    //object with animation controller on, which you want to animate
     public AudioClip jumpSound;                    //play when jumping
     public AudioClip landSound;                    //play when landing on ground
     
     //movement
     public float accel = 70f;                    //acceleration/deceleration in air or on the ground
     public float airAccel = 18f;            
     public float decel = 7.6f;
     public float airDecel = 1.1f;
     [Range(0f, 5f)]
     public float rotateSpeed = 0.7f, airRotateSpeed = 0.4f;    //how fast to rotate on the ground, how fast to rotate in the air
     public float maxSpeed = 9;                                //maximum speed of movement in X/Z axis
     public float slopeLimit = 40, slideAmount = 35;            //maximum angle of slopes you can walk on, how fast to slide down slopes you can't
     public float movingPlatformFriction = 7.7f;                //you'll need to tweak this to get the player to stay on moving platforms properly
     
     //jumping
     public Vector3 jumpForce =  new Vector3(0, 13, 0);        //normal jump force
     public Vector3 secondJumpForce = new Vector3(0, 13, 0); //the force of a 2nd consecutive jump
     public Vector3 thirdJumpForce = new Vector3(0, 13, 0);    //the force of a 3rd consecutive jump
     public float jumpDelay = 0.1f;                            //how fast you need to jump after hitting the ground, to do the next type of jump
     public float jumpLeniancy = 0.17f;                        //how early before hitting the ground you can press jump, and still have it work
     [HideInInspector]
     public int onEnemyBounce;                    
     
     private int onJump;
     private bool grounded;
     private Transform[] floorCheckers;
     private Quaternion screenMovementSpace;
     private float airPressTime, groundedCount, curAccel, curDecel, curRotateSpeed, slope;
     private Vector3 direction, moveDirection, screenMovementForward, screenMovementRight, movingObjSpeed;
     
     private CharacterMotor characterMotor;
     private EnemyAI enemyAI;
     private DealDamage dealDamage;
     
     //setup
     void Awake()
     {
         //create single floorcheck in centre of object, if none are assigned
         if(!floorChecks)
         {
             floorChecks = new GameObject().transform;
             floorChecks.name = "FloorChecks";
             floorChecks.parent = transform;
             floorChecks.position = transform.position;
             GameObject check = new GameObject();
             check.name = "Check1";
             check.transform.parent = floorChecks;
             check.transform.position = transform.position;
             Debug.LogWarning("No 'floorChecks' assigned to PlayerMove script, so a single floorcheck has been created", floorChecks);
         }
         //assign player tag if not already
         if(tag != "Player")
         {
             tag = "Player";
             Debug.LogWarning ("PlayerMove script assigned to object without the tag 'Player', tag has been assigned automatically", transform);
         }
         //usual setup
         mainCam = GameObject.FindGameObjectWithTag("MainCamera").transform;
         dealDamage = GetComponent<DealDamage>();
         characterMotor = GetComponent<CharacterMotor>();
         //gets child objects of floorcheckers, and puts them in an array
         //later these are used to raycast downward and see if we are on the ground
         floorCheckers = new Transform[floorChecks.childCount];
         for (int i=0; i < floorCheckers.Length; i++)
             floorCheckers[i] = floorChecks.GetChild(i);
     }
     
     //get state of player, values and input
     void Update()
     {    
         //handle jumping
         JumpCalculations ();
         //adjust movement values if we're in the air or on the ground
         curAccel = (grounded) ? accel : airAccel;
         curDecel = (grounded) ? decel : airDecel;
         curRotateSpeed = (grounded) ? rotateSpeed : airRotateSpeed;
                 
         //get movement axis relative to camera
         screenMovementSpace = Quaternion.Euler (0, mainCam.eulerAngles.y, 0);
         screenMovementForward = screenMovementSpace * Vector3.forward;
         screenMovementRight = screenMovementSpace * Vector3.right;
         
         //get movement input, set direction to move in
         float h = Input.GetAxisRaw ("Horizontal");
         float v = Input.GetAxisRaw ("Vertical");
         
         //only apply vertical input to movemement, if player is not sidescroller
         if(!sidescroller)
             direction = (screenMovementForward * v) + (screenMovementRight * h);
         else
             direction = Vector3.right * h;
         moveDirection = transform.position + direction;
     }
     
     //apply correct player movement (fixedUpdate for physics calculations)
     void FixedUpdate() 
     {
         //are we grounded
         grounded = IsGrounded ();
         //move, rotate, manage speed
         characterMotor.MoveTo (moveDirection, curAccel, 0.7f, true);
         if (rotateSpeed != 0 && direction.magnitude != 0)
             characterMotor.RotateToDirection (moveDirection , curRotateSpeed * 5, true);
         characterMotor.ManageSpeed (curDecel, maxSpeed + movingObjSpeed.magnitude, true);
         //set animation values
         if(animator)
         {
             animator.SetFloat("DistanceToTarget", characterMotor.DistanceToTarget);
             animator.SetBool("Grounded", grounded);
             animator.SetFloat("YVelocity", GetComponent<Rigidbody>().velocity.y);
         }
     }
     
     //prevents rigidbody from sliding down slight slopes (read notes in characterMotor class for more info on friction)
     void OnCollisionStay(Collision other)
     {
         //only stop movement on slight slopes if we aren't being touched by anything else
         if (other.collider.tag != "Untagged" || grounded == false)
             return;
         //if no movement should be happening, stop player moving in Z/X axis
         if(direction.magnitude == 0 && slope < slopeLimit && GetComponent<Rigidbody>().velocity.magnitude < 2)
         {
             //it's usually not a good idea to alter a rigidbodies velocity every frame
             //but this is the cleanest way i could think of, and we have a lot of checks beforehand, so it shou
             GetComponent<Rigidbody>().velocity = Vector3.zero;
         }
     }
     
     //returns whether we are on the ground or not
     //also: bouncing on enemies, keeping player on moving platforms and slope checking
     private bool IsGrounded() 
     {
         //get distance to ground, from centre of collider (where floorcheckers should be)
         float dist = GetComponent<Collider>().bounds.extents.y;
         //check whats at players feet, at each floorcheckers position
         foreach (Transform check in floorCheckers)
         {
             RaycastHit hit;
             if(Physics.Raycast(check.position, Vector3.down, out hit, dist + 0.05f))
             {
                 if(!hit.transform.GetComponent<Collider>().isTrigger)
                 {
                     //slope control
                     slope = Vector3.Angle (hit.normal, Vector3.up);
                     //slide down slopes
                     if(slope > slopeLimit && hit.transform.tag != "Pushable")
                     {
                         Vector3 slide = new Vector3(0f, -slideAmount, 0f);
                         GetComponent<Rigidbody>().AddForce (slide, ForceMode.Force);
                     }
                     //enemy bouncing
                     if (hit.transform.tag == "Enemy" && GetComponent<Rigidbody>().velocity.y < 0)
                     {
                         enemyAI = hit.transform.GetComponent<EnemyAI>();
                         enemyAI.BouncedOn();
                         onEnemyBounce ++;
                         dealDamage.Attack(hit.transform.gameObject, 1, 0f, 0f);
                     }
                     else
                         onEnemyBounce = 0;
                     //moving platforms
                     if (hit.transform.tag == "MovingPlatform" || hit.transform.tag == "Pushable")
                     {
                         movingObjSpeed = hit.transform.GetComponent<Rigidbody>().velocity;
                         movingObjSpeed.y = 0f;
                         //9.5f is a magic number, if youre not moving properly on platforms, experiment with this number
                         GetComponent<Rigidbody>().AddForce(movingObjSpeed * movingPlatformFriction * Time.fixedDeltaTime, ForceMode.VelocityChange);
                     }
                     else
                     {
                         movingObjSpeed = Vector3.zero;
                     }
                     //yes our feet are on something
                     return true;
                 }
             }
         }
         movingObjSpeed = Vector3.zero;
         //no none of the floorchecks hit anything, we must be in the air (or water)
         return false;
     }
     
     //jumping
     private void JumpCalculations()
     {
         //keep how long we have been on the ground
         groundedCount = (grounded) ? groundedCount += Time.deltaTime : 0f;
         
         //play landing sound
         if(groundedCount < 0.25 && groundedCount != 0 && !GetComponent<AudioSource>().isPlaying && landSound && GetComponent<Rigidbody>().velocity.y < 1)
         {
             GetComponent<AudioSource>().volume = Mathf.Abs(GetComponent<Rigidbody>().velocity.y)/40;
             GetComponent<AudioSource>().clip = landSound;
             GetComponent<AudioSource>().Play ();
         }
         //if we press jump in the air, save the time
         if (Input.GetButtonDown ("Jump") && !grounded)
             airPressTime = Time.time;
         
         //if were on ground within slope limit
         if (grounded && slope < slopeLimit)
         {
             //and we press jump, or we pressed jump justt before hitting the ground
             if (Input.GetButtonDown ("Jump") || airPressTime + jumpLeniancy > Time.time)
             {    
                 //increment our jump type if we haven't been on the ground for long
                 onJump = (groundedCount < jumpDelay) ? Mathf.Min(2, onJump + 1) : 0;
                 //execute the correct jump (like in mario64, jumping 3 times quickly will do higher jumps)
                 if (onJump == 0)
                         Jump (jumpForce);
                 else if (onJump == 1)
                         Jump (secondJumpForce);
                 else if (onJump == 2)
                         Jump (thirdJumpForce);
             }
         }
     }
     
     //push player at jump force
     public void Jump(Vector3 jumpVelocity)
     {
         if(jumpSound)
         {
             GetComponent<AudioSource>().volume = 1;
             GetComponent<AudioSource>().clip = jumpSound;
             GetComponent<AudioSource>().Play ();
         }
         GetComponent<Rigidbody>().velocity = new Vector3(GetComponent<Rigidbody>().velocity.x, 0f, GetComponent<Rigidbody>().velocity.z);
         GetComponent<Rigidbody>().AddRelativeForce (jumpVelocity, ForceMode.Impulse);
         airPressTime = 0f;
     }
 }