How to access random item in list?

1. Create an instance of Random class somewhere. Note that it's pretty important not to create a new instance each time you need a random number. You should reuse the old instance to achieve uniformity in the generated numbers. You can have a static field somewhere (be careful about thread safety issues):

   static Random rnd = new Random();
   

2. Ask the Random instance to give you a random number with the maximum of the number of items in the ArrayList:

   int r = rnd.Next(list.Count);
   

3. Display the string:

   MessageBox.Show((string)list[r]);
   

I usually use this little collection of extension methods:

public static class EnumerableExtension
{
    public static T PickRandom<T>(this IEnumerable<T> source)
    {
        return source.PickRandom(1).Single();
    }

    public static IEnumerable<T> PickRandom<T>(this IEnumerable<T> source, int count)
    {
        return source.Shuffle().Take(count);
    }

    public static IEnumerable<T> Shuffle<T>(this IEnumerable<T> source)
    {
        return source.OrderBy(x => Guid.NewGuid());
    }
}

For a strongly typed list, this would allow you to write:

var strings = new List<string>();
var randomString = strings.PickRandom();

If all you have is an ArrayList, you can cast it:

var strings = myArrayList.Cast<string>();

You can do:

list.OrderBy(x => Guid.NewGuid()).FirstOrDefault()

Create a Random instance:

Random rnd = new Random();

Fetch a random string:

string s = arraylist[rnd.Next(arraylist.Count)];

Remember though, that if you do this frequently you should re-use the Random object. Put it as a static field in the class so it's initialized only once and then access it.

I'll suggest different approach, If the order of the items inside the list is not important at extraction (and each item should be selected only once), then instead of a List you can use a ConcurrentBag which is a thread-safe, unordered collection of objects:

var bag = new ConcurrentBag<string>();
bag.Add("Foo");
bag.Add("Boo");
bag.Add("Zoo");

The EventHandler:

string result;
if (bag.TryTake(out result))
{
    MessageBox.Show(result);
}

The TryTake will attempt to extract an "random" object from the unordered collection.

Printing randomly country name from JSON file.
Model:

public class Country
    {
        public string Name { get; set; }
        public string Code { get; set; }
    }

Implementaton:

string filePath = Path.GetFullPath(Path.Combine(Environment.CurrentDirectory, @"..\..\..\")) + @"Data\Country.json";
            string _countryJson = File.ReadAllText(filePath);
            var _country = JsonConvert.DeserializeObject<List<Country>>(_countryJson);


            int index = random.Next(_country.Count);
            Console.WriteLine(_country[index].Name);

Why not[2]:

public static T GetRandom<T>(this List<T> list)
{
     return list[(int)(DateTime.Now.Ticks%list.Count)];
}