for class countryclassinfolink:

$(".classcard").fadeOut("slow"); is working
$(".classdetails").fadein("slow");is not working

<html>
    <head>
    <style>
    .section {
        background: none repeat scroll 0 0 #FFFFFF;
        border-radius: 10px 10px 0 0;
        margin: 0 0 30px;
        width: 725px;
        padding: 0 0 20px;
        position: relative;
        z-index: 100;
    }
    .section.seminars .theta_wrap {
        border-bottom: 1px solid #A6CBD9;
        float: left;
        font-size: 13px;
        margin: 5px 15px;
        padding: 10px 3px 5px;
        width: 197px;
    }
    </style>
    <script type="text/javascript" src="http://code.jquery.com/jquery-1.8.0.min.js"></script>
    <script type="text/javascript">
    $(document).ready(function(){
        $(".countryclassinfolink").click(function () {
            $(".classcard").fadeOut("slow");
            $(".classdetails").fadein("slow");
        });

        $(".countryclassinfolink2").click(function(){
            $(".classdetails").fadeOut("slow");
            $(".classcard").fadein("slow");                                            
        });
    });

    </script>
    </head>
    <body>
    <div class="section seminars">
      <h2><span>USA Seminars</span></h2>
      <div id="country_seminars" class="body" style="display: block;">
        <div class="theta_wrap">
          <div class="practioners">
            <div class="classcard" id="">
              <p> <span class="date">06/10/2013</span> Niskayuna, NY<br>
                <a class="countryclassinfolink" href="#">Advanced DNA</a> </p>
            </div>
            <div style="display:none;" class="classdetails" id="">
              <div class="searchresults result" style="border-bottom: none;width:650px;"><a style="float:right;" class="countryclassinfolink2" href="#">Return</a>
                <div class="resultheader">
                  <div style="background-image:none;float:none;" class="name">Advanced DNA</div>
                  <div style="background-image:none;" class="name">Anana Integre</div>
                  <div class="icon"><img src="images/practitioner-icon.gif"></div>
                  <div class="icon"><img src="images/instructor-icon.gif"></div>
                </div>
                <div class="image"><img border="0" alt="" src="/images/specialistImages/thumb_1294779133.jpg"></div>
                <div style="width: 400px;" class="info">
                  <div class="text_desc_div">Niskayuna, NY<br>
                    <strong>Phone:</strong><br>
                    831-246-1790<br>
                    <strong>Email:</strong><br>
                    <a href="mailTo:miraclewrkr@gmail.com">miraclewrkr@gmail.com</a><br>
                    <strong>Website:</strong><br>
                    <a target="_blank" href="http://www.thetahealingwitness.com">www.thetahealingwitness.com</a><br>
                    <strong>Cost:</strong><br>
                    $&nbsp;575.00<br>
                    <strong>Notes:</strong><br>
                    <br>
                    <strong>Dates:</strong><br>
                    06/10/2013<br>
                    06/12/2013<br>
                  </div>
                  <!-- text desc part-->
                </div>
              </div>
            </div>
            <!--Hide part-->
          </div>
        </div>
        <div class="clear"></div>
      </div>
    </div>
    </body>
    </html>

I didn't review your code, but you referenced fadein()... Shoukd be fadeIn(). It's case sensitive.

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