This sample fetches accounts using a jQuery ajax method. On thing to note is that you need to set the header in the call to make the work.
$.ajax({
url: Xrm.Page.context.getClientUrl() + '/api/data/v8.0/accounts',
headers: {
'Accept': 'Application/json'
}
}).done(function (result) {
var accounts = result.value;
});