Ok, here is my AJAX call in its entirety (stopped at the success property, because I assume this is where people diverge):
$.ajax({
url: 'https://en.wikipedia.org/w/api.php?action=query&format=json&list=search&srsearch=' + $('#searchform').val() + '&srnamespace=0&srprop=snippet',
data: {
format: 'json'
},
dataType: 'jsonp',
success: function (data){//stuff you do with the data
});