This post is specifically created for my reference.
These are the main methods that I have been using to make ajax calls to the server using jquery.

Populating Dropdown list with json:

$.getJSON('/Dashboard/GetAthletesByTeamID/' + $("#TeamId > option:selected").attr("value"), 
             function (data) { 
             //Clear the Model list
             //Foreach Model in the list, add a model option from the data returned
             $.each(data, function (index, optionData) {
               $("#ddlAthlete").append("" + optionData.Value + "");

Dump return html into specific div:

    url: "/Dashboard/GetAthletesTreeByAthleteId/" + $("#AthleteId > option:selected").attr("value"),
    type: 'GET', dataType: 'html',
    success: function doSubmitSuccess(result) {

Posting Information and getting json back

   cache: false });
   var selectedItem = $(this).val();
        { id: selectedItem,
          extra: data },
          function (data) {
            if (data.length > 0) {
               //do your stuff