You can either parent your camera to character (or vice versa) to make it attached, or you can update camera position from script based on character's position.

After a few hours of messing around with various scripting suggestions, I got this working for controlling a simple cube.

I learned the hard way that integer math can destroy Time.deltaTime, and that editing a script does NOT change the copy of the script that is attached to a character.

// I called this script move.js and added it to my main character.

var sspeed = 5.0; // speed that the 
var turnSpeed : float = 90.0; // degrees per second.
    //Good to have ".0" or explicit "float" because int math kills the turning!!

function Update () {
    // Move Forward or Backward... 
        // [default keys: w/s/fwd/bak = "Vertical" (z axis)]
        var z = Input.GetAxis("Vertical") * Time.deltaTime * sspeed; 
        transform.Translate(0, 0, z);

    // Turn Left or Right...  
        // [default keys: a/d/left/right = "Horizontal" (x axis)]
        // beware: MUST do the math with explicit floats to avoid int round off!
        var turnAngle : float = turnSpeed * Input.GetAxis("Horizontal") * Time.deltaTime;
    transform.Rotate (0, turnAngle, 0);
} // Update( )