Firstly some points to note about arrays in C#:

• C# arrays are zero indexed, meaning 0 is the first index.
• Array elements are referenced using square brackets [].
• In declarations the square brackets ([]) come after the type, not the identifier. e.g. string[] cites; and not string cities[];
• An array can hold other arrays or objects as well as common data objects.
• Initialisation can be done at the same time as declaration.

Below is a simple console application that demonstrates Single Dimension arrays, Multiple Dimension arrays and Arrays of arrays, also known as Ragged arrays or Jagged Arrays.

using System;

namespace ArraysSample
{
    class Program
    {
        static void Main(string[] args)
        {
            // single dimension
            int[] ages = new int[5];
            ages[0] = 3;
            ages[1] = 6;
            ages[2] = 20;
            ages[3] = 34;
            ages[4] = 67;

            Console.WriteLine("Single Dimensional Array");
            for (int ageLoop = 0; ageLoop < ages.Length; ageLoop++)
            {
                Console.WriteLine(string.Format("Item {0}: {1}", ageLoop, ages[ageLoop]));
            }

            Console.Write("\n\nMulti Dimensional Array\n");

            // multi dimensional
            string[,] names = new string[2, 2];
            names[0, 0] = "Andrew";
            names[0, 1] = "Bobby";
            names[1, 0] = "Susan";
            names[1, 1] = "Peter";

            Console.WriteLine("Row\tCol\tValue");
            for (int row = 0; row < names.GetLength(0); row++)
            {
                for (int col = 0; col < names.GetLength(row); col++)
                {
                    Console.WriteLine(String.Format("{0}\t{1}\t{2}", row, col, names[row, col]));
                }
            }

            Console.Write("\n\nArray of Arrays\n");

            // Array of arrays
            string[][] days = new string[2][];

            days[0] = new string[2];
            days[0][0] = "Monday";
            days[0][1] = "Wednesday";

            days[1] = new string[4];
            days[1][0] = "Tuesday";
            days[1][1] = "Friday";
            days[1][2] = "Saturday";
            days[1][3] = "Sunday";

            Console.WriteLine("Row\tCol\tValue");
            for (int row = 0; row < days.GetLength(0); row++)
            {
                for (int col = 0; col < days[row].GetLength(0); col++)
                {
                    Console.WriteLine(String.Format("{0}\t{1}\t{2}", row, col, days[row][col]));
                }
            }

            if (System.Diagnostics.Debugger.IsAttached)
            {
                System.Diagnostics.Debugger.Break();
            }
        }
    }
}

Output from the above application when run is:

Single Dimensional Array
Item 0: 3
Item 1: 6
Item 2: 20
Item 3: 34
Item 4: 67
Multi Dimensional Array
Row     Col     Value
0       0       Andrew
0       1       Bobby
1       0       Susan
1       1       Peter
Array of Arrays
Row     Col     Value
0       0       Monday
0       1       Wednesday
1       0       Tuesday
1       1       Friday
1       2       Saturday
1       3       Sunday

In the above exmaples the array elements have been set long hand, an element at a time.  It is possible to initialise an array at the same time as the declaration.  Obviously we would only do this if the values were fixed and we knew them from the start.

// single dimension array
int[] ages = new int[4] = {1, 2, 3, 4};
string[] names = new string[4] = {"Andrew", "Bobby", "Susan", "Peter"};

// multi dimension array
int[,] numbers = new int{1, 9] { {2, 8}, {3, 7}, {4, 6}, {5, 5} };
string[,] siblings = new string[2, 2] { {"Mike","Amy"}, {"Mary","Albert"} };

// array of Arrays
int[][] days = new int[2][] { new int[] {1, 2, 3}, new int[] {98, 99, 100} };

Instead of using a for loop to iterate an arry a foreach loop can be used.  This is not as useful on multi dimension arrays because the whole array is treated as one single list.

// single dimension array
foreach (int age in ages)
{
    Console.WriteLine(string.Format("Item {0}", age));
}

// multi dimension array
foreach (string name in names)
{
    Console.WriteLine(name);
}

// array of arrays
foreach (string[] d in days)
{
    foreach (string day in d)
    {
        Console.WriteLine(day);
    }
}

You will notice in the top example the single dimensional array example uses the Length property to get the length of the array.  In the other examples the GetLength method has been used.  The Length property will give the total number of elements in an array  which is 5 in the ages array and 4 in the names array.  The GetLength method accepts an array index (integer) and will return the length of the particular element which in the days array is 2 for the first element and 4 for the second.

ages.Length //5 - Full length of array
ages.GetLength(0) //5 - single dimension so full length of array
ages.GetUpperBound(0) //4 - Index range is 0 to 4
names.Length // 4 - Full length of array
names.GetLength(0) // 2 - Length of elements in first dimension
names.GetUpperBound(0)// 1 - first dimensions index range is 0 to 1
days.Length // 2 - Length of main array	2
days.GetLength(0) // 2 - Length of array in first element
days.GetUpperBound(0) // 1 - Array index range is 0 to 1
days[0].GetUpperBound(0) // 1 - First element array index range is 0 to 1
days[1].GetUpperBound(0) // 3 - Second element array index range is 0 to 3
days[1].Length // 4 - Length of array in First element
days[1].GetUpperBound(0) // 3 - Second element array index range is 0 to 3

An example console application is available from Github here