JSON to HTML table using ASP.NET Web API

The answer from the Web API is JSON, which is a JavaScript object serialized as string (JSON is JavaScript Object Notation). What you need to do is to

1. get the JSON answer form the server
2. convert it to a JavaScript object
3. and use some kind of template or MV* framework to show it easyly in a table.

For 1, you need to make the query using AJAX to get the JSON response.

For 2 you can use the JSON functionality of the Browser (JSON.parse) or a JSON library if the browser is too old (for example JSON 3).

However, if you use a framework like jQuery to make the Ajax requests, you can directly get the JavaScript object.

For 3, you can use JavaScript template libraries like Handlebars or Mustache, or an MV* library like the MVVM Knockout.JS

Pseudocode:

$.post('service url', {twitter_handle: 'value'}).done(function(data) {
   // Use any of the template or MV* solution to generate the HTML
   // from the data object and the template
});

Alternatively, you can use any of the available grid JavaScript libraries, like the jQuery plugins datatables or SlickGrid or jqGrid.

As you can see, there a a lot of options, but the basic idea is explained in the 3 points at the beginning of this answer.