how to change text value within an element?

This should do it:

$('.post-read a').html('continue reading');

Through the text property in jQuery that changes the inner text of the <tag>

$(document).ready(function () {
    $('.postread a').text("your new text here ");
}

$('.post-read a').html("continue reading")

Do it with jQuery inside of a document ready handler ($(fn))...

$('.post-read a').text('continue reading');

jsFiddle.

For the sake of it, here is how to do it without jQuery....

var anchor = document.getElementsByClassName('post-read')[0].getElementsByTagName('a')[0],
    textProperty;

if (anchor.textContent) {
    textProperty = 'textContent';
} else if (anchor.innerText) {
    textProperty = 'innerText';
}
anchor[textProperty] = 'continue reading';

jsFiddle.

This will work good for your piece of HTML, but it isn't too generic.

If you don't care about setting innerText property, you could use...

anchor.textContent = anchor.innerText = 'continue reading';

I wouldn't recommend it though.