jQuery - Repeating same actions on different DOM elements
You're right, you are violating some DRY rules, so lets clean it up. First, I would cache some of the selectors you're calling.

var $info = $('.userInfo');
var $details = $info.find('.details');
var $detailsExpand = $info.find('.expandUserDetails');


Then I would take a look at some of the toggle options that jQuery offers, mainly:


toggleClass
slideToggle


This will save you the trouble of having to use .addClass, .removeClass, slideUp, and slideDown.

For example, you have:

if ($('.paymentInfo .details').is(':hidden')) {
    $('.paymentInfo .details').addClass('active').slideDown();
    $('.paymentInfo .expandPaymentDetails').removeClass('down').addClass('up').addClass('active');
} else {
    $('.paymentInfo .expandPaymentDetails').removeClass('up').addClass('down').removeClass('active');
    $('.paymentInfo .details').removeClass('active').slideUp();
}


We can remove that else statement, and just let our new toggle methods handle the adding/removing.

if ($details.is(':hidden')) {
    $details
        .toggleClass('active', true) // true means the class will be added
        .slideToggle();

    $detailsExpand
        .toggleClass('down', false)  // false means the class will be removed
        .toggleClass('up', true)
        .toggleClass('active', true);
}


Lastly, and this might be overkill, you could try creating a jQuery plugin:

$.fn.toggleDetails = function (options) {
    var settings = $.extend({
        infoClass: null,
        expandClass: null
    }, options);

    var $info = $(settings.infoClass);

    var $details = $info.find('.details');
    var $detailsExpand = $info.find(settings.expandClass);

    if ($details.is(':hidden')) {
        $details
            .toggleClass('active', true)
            .slideToggle();

        $detailsExpand
            .toggleClass('down', false)
            .toggleClass('up', true)
            .toggleClass('active', true);
    }
};


And then applying your new plugin would be as easy as calling the .toggleDetails method on your selected elements, and providing both an infoClass and expandClass.

$('.user .expandDetails a').toggleDetails({
    infoClass: '.userInfo',
    expandClass: '.expandUserDetails'
});

$('.user .paymentDetails a').toggleDetails({
    infoClass: '.paymentInfo',
    expandClass: '.expandPaymentDetails'
});


Caveats:


This code hasn't been tested.
I'm not sure how to assign a down or up to slideToggle. I would have expected a similar true/false parameter similar to toggleClass.