First of all, you have to make sure that the JSON code is valid.
After that, I would recommend using a JavaScript library such as jQuery or Prototype if you can because these things are handled well in those libraries.
On the other hand, if you don't want to use a library and you can vouch for the validity of the JSON object, I would simply wrap the string in an anonymous function and use the eval function.
This is not recommended if you are getting the JSON object from another source that isn't absolutely trusted because the eval function allows for renegade code if you will.
Here is an example of using the eval function:
var strJSON = '{"result":true,"count":1}';
var objJSON = eval("(function(){return " + strJSON + ";})()");
alert(objJSON.result);
alert(objJSON.count);
If you control what browser is being used or you are not worried people with an older browser, you can always use the JSON.parse method.
This is really the ideal solution for the future.