In your Page_Load you will want to clear out the normal output and write your own, for example:
string json = "{\"name\":\"Joe\"}";
Response.Clear();
Response.ContentType = "application/json; charset=utf-8";
Response.Write(json);
Response.End();
To convert a C# object to JSON you can use a library such as Json.NET.
Instead of getting your .aspx page to output JSON though, consider using a Web Service (asmx) or WCF, both of which can output JSON.