You have a few options. You can disable ViewState, or you can use "plain AJAX".
If you choose to use "plain AJAX", you can write your low level JavaScript code or use libraries such as jQuery to make the AJAX calls easier.
On the server side, you'll need to expose some kind of endpoint for the AJAX calls to communicate to. Some people use WebMethod, but that has been deprecated and I would avoid this approach. You can use ASP.NET Web API in .NET 4.5, or in any version of .NET you can use handlers or generic handlers (.ashx) to expose endpoints.