Using Forms Authentication with ASP.NET AJAX:
You can use the Microsoft AJAX Library application authentication service to verify credentials that are stored as part of the ASP.NET membership service.
You can access the authentication service from client script by using the AuthenticationService class, which supports the following methods:
login. This method validates the user credentials by using the default membership provider. If the credentials are verified, the method sends a forms authentication cookie to the browser. Most ASP.NET AJAX applications will use the login method, because forms-authenticated applications require an authentication cookie in the browser.
logout. This method clears the forms authentication cookie.
Configuring the Server:
The server provides the infrastructure to process the identification credentials such as name and password from a user, and to validate those credentials. The forms authentication feature in ASP.NET enables you to authenticate the user's login name and password users by using a login form. If the application authenticates the request, the server issues a ticket that contains a key for reestablishing the user identity in subsequent requests.
See more details: http://msdn.microsoft.com/en-us/library/bb398896.aspx