How to change Dates format from text (Json string) in C# (or how to get date values from a long string)

JSON can be parsed into objects that look like the JSON structure. For example,

{
    days: [
        {name: 'monday', value: 5}, 
        {name: 'tuesday', value: 7}
    ],
    week: 18
}

Will become an object with two properties: days and week. You can then use the object just like any other C# object:

Console.WriteLine(parsed.week); //Prints 18
Console.WriteLine(parsed.days[0].name); //Prints 'Monday'
Console.WriteLine(parsed.days[1].value); //Prints 7

So, on to your actual data:

Your JSON example appears to be slightly malformed, so I modified the start a little bit to make a simple example.

Using JSON.Net (can be installed with NuGet), it can be done like this:

var jsonString = "{data: [{'ItemId':340,'LineId':340,'ItemName':'Trim 1_5A','ItemType':1},{'ItemId':341,'LineId':341,'ItemName':'Trim 1_5B','ItemType':1}],'Success':true,'Errors':[],'OperationCanceled':false,'ErrorsConcatented':'','ResponseTime':'/Date(1425474069569)/'}";
dynamic data = JValue.Parse(jsonString);

Console.WriteLine(data.ResponseTime); //this is your DateTime object
Console.WriteLine(data.ResponseTime.ToString("mm-dd-yyyy")); //Formatted like you wanted it

EDIT: Without packages. How about using System.Web.Helpers.Json?

dynamic data = System.Web.Helpers.Json.Decode(jsonString);

Console.WriteLine(data.ResponseTime); ///Date(1425474069569)/

//Now we need to create a DateTime object from this string.
var timeString = data.ResponseTime.Replace("/Date(", "").Replace(")/",""); //Remove the wrapping
var seconds = long.Parse(timeString)/1000; //Parse the number, and turn it into seconds (it was milliseconds)
var date = new DateTime(1970,1,1,0,0,0).AddSeconds(seconds); //Create a new DateTime object starting on the Unix date, and add the seconds
Console.WriteLine(date.ToString("dd-MM-yyyy"));

And if you don't even have System.Web.Helpers, you could also parse the string manually (Regex.Split, String.Split, String.Replace, etc), and use the above method of creating a DateTime object from the date string.