Use the same methods to secure the request as you would use normally, since AJAX is just a HTTP request. But keep in mind that besides checking for the "normal" things (check the users privileges, sanitize the data, etc), also check if he really made the request or if he was tricked (for example a link on another page). To do that, include a CSRF-token in each AJAX request and validate it on the server side (see What is the correct way to implement anti-CSRF form tokens?). Though it is recommended that a CSRF token is used even in normal requests.
Another thing is that depending on what you do with on the client side, also sanitize the data there. Else an attacker could inject harmful code into the page. This is especially important if you get data from a third party, but best do it for all input.