"Pet Like" Follow

Would somebody either explain how I'd go about it or tell me how to have an object follow another object and stop once within a certain distance? Imagine a pet following a character, something basic like that.

var minDist;
var speed;

function Update(){
    chase();
}
function chase(){
    //Find which way player is facing, make the "pet" point to it and move at speed*1
    checkDistance();
}
function checkDistance(){
    //var distance = distance between player and pet;
    if(distance <= minDist){
        speed = 0;
    }
    else{
        speed = //Whatever your speed is...
    }
}

Something like this should work =).