Somehow all examples, while work well, are overcomplicated:
- They use new Array(), which is an overkill (and an overhead) for a simple associative array (AKA dictionary).
- The better ones use new Object(). It works fine, but why all this extra typing?
This question is tagged "beginner", so let's make it simple.
The über-simple way to use a dictionary in JavaScript or "Why doesn't JavaScript have a special dictionary object?":
// Create an empty associative array (in JavaScript it is called ... Object)
var dict = {};   // Huh? {} is a shortcut for "new Object()"
// Add a key named fred with value 42
dict.fred = 42;  // We can do that because "fred" is a constant
                 // and conforms to id rules
// Add a key named 2bob2 with value "twins!"
dict["2bob2"] = "twins!";  // We use the subscript notation because
                           // the key is arbitrary (not id)
// Add an arbitrary dynamic key with a dynamic value
var key = ..., // Insanely complex calculations for the key
    val = ...; // Insanely complex calculations for the value
dict[key] = val;
// Read value of "fred"
val = dict.fred;
// Read value of 2bob2
val = dict["2bob2"];
// Read value of our cool secret key
val = dict[key];
Now let's change values:
// Change the value of fred
dict.fred = "astra";
// The assignment creates and/or replaces key-value pairs
// Change the value of 2bob2
dict["2bob2"] = [1, 2, 3];  // Any legal value can be used
// Change value of our secret key
dict[key] = undefined;
// Contrary to popular beliefs, assigning "undefined" does not remove the key
// Go over all keys and values in our dictionary
for (key in dict) {
  // A for-in loop goes over all properties, including inherited properties
  // Let's use only our own properties
  if (dict.hasOwnProperty(key)) {
    console.log("key = " + key + ", value = " + dict[key]);
  }
}
Deleting values is easy too:
// Let's delete fred
delete dict.fred;
// fred is removed, but the rest is still intact
// Let's delete 2bob2
delete dict["2bob2"];
// Let's delete our secret key
delete dict[key];
// Now dict is empty
// Let's replace it, recreating all original data
dict = {
  fred:    42,
  "2bob2": "twins!"
  // We can't add the original secret key because it was dynamic, but
  // we can only add static keys
  // ...
  // oh well
  temp1:   val
};
// Let's rename temp1 into our secret key:
if (key != "temp1") {
  dict[key] = dict.temp1; // Copy the value
  delete dict.temp1;      // Kill the old key
} else {
  // Do nothing; we are good ;-)
}