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The method for retrieving the value of an HTML tag element and saving it within a variable is:

1. Select the HTML element using JavaScript or jQuery selectors.
2. Use the .value property to get the value of the selected element.
3. Save the value in a variable using the assignment operator (=).

Here is an example:

// Select the HTML input element with ID "name"
var nameInput = document.getElementById("name");

// Get the value of the input element
var name = nameInput.value;

// Output the value of the input element
console.log(name);

In the example above, we first select the HTML input element with ID "name" using the getElementById() method. We then retrieve the value of the input element using the .value property and save it in a variable called name. Finally, we output the value of the input element to the console using console.log().