How can I move the character like 2D games?

Add a Rigidbody2D and a Collider2D (for example, a CircleCollider2D) to your player GameObject. Then, add a script that has this implementation for starters:

 private Rigidbody2D rb2d;
 public float speed;

 private void Awake()
 {
     rb2d = GetComponent<Rigidbody2D>();
 }

 private void FixedUpdate()
 {
     // Put input values in a Vector2
     var input = new Vector2(Input.GetAxis("Horizontal"), Input.GetAxis("Vertical"));
     // Clamp the vector to not have a length over 1,
     // otherwise running diagonally would be faster
     input = Vector2.ClampMagnitude(input, 1);

     // Set the velocity of the Rigidbody2D so it moves in that direction
     rb2d.velocity = input * speed * Time.deltaTime;
 }

The Time.deltaTime factor is optional, but i personally like speed to be in meters/second, which this enables.

Of course, feel free to experiment with this script to get a feel for what it does.