How do I sort a two-dimensional (rectangular) array in C#?

Load your two-dimensional string array into an actual DataTable (System.Data.DataTable), and then use the DataTable object's Select() method to generate a sorted array of DataRow objects (or use a DataView for a similar effect).

// assumes stringdata[row, col] is your 2D string array
DataTable dt = new DataTable();
// assumes first row contains column names:
for (int col = 0; col < stringdata.GetLength(1); col++)
{
    dt.Columns.Add(stringdata[0, col]);
}
// load data from string array to data table:
for (rowindex = 1; rowindex < stringdata.GetLength(0); rowindex++)
{
    DataRow row = dt.NewRow();
    for (int col = 0; col < stringdata.GetLength(1); col++)
    {
        row[col] = stringdata[rowindex, col];
    }
    dt.Rows.Add(row);
}
// sort by third column:
DataRow[] sortedrows = dt.Select("", "3");
// sort by column name, descending:
sortedrows = dt.Select("", "COLUMN3 DESC");

You could also write your own method to sort a two-dimensional array. Both approaches would be useful learning experiences, but the DataTable approach would get you started on learning a better way of handling tables of data in a C# application.

Can I check - do you mean a rectangular array ([,])or a jagged array ([][])?

It is quite easy to sort a jagged array; I have a discussion on that here. Obviously in this case the Comparison<T> would involve a column instead of sorting by ordinal - but very similar.

Sorting a rectangular array is trickier... I'd probably be tempted to copy the data out into either a rectangular array or a List<T[]>, and sort there, then copy back.

Here's an example using a jagged array:

static void Main()
{  // could just as easily be string...
    int[][] data = new int[][] { 
        new int[] {1,2,3}, 
        new int[] {2,3,4}, 
        new int[] {2,4,1} 
    }; 
    Sort<int>(data, 2); 
} 
private static void Sort<T>(T[][] data, int col) 
{ 
    Comparer<T> comparer = Comparer<T>.Default;
    Array.Sort<T[]>(data, (x,y) => comparer.Compare(x[col],y[col])); 
} 

For working with a rectangular array... well, here is some code to swap between the two on the fly...

static T[][] ToJagged<T>(this T[,] array) {
    int height = array.GetLength(0), width = array.GetLength(1);
    T[][] jagged = new T[height][];

    for (int i = 0; i < height; i++)
    {
        T[] row = new T[width];
        for (int j = 0; j < width; j++)
        {
            row[j] = array[i, j];
        }
        jagged[i] = row;
    }
    return jagged;
}
static T[,] ToRectangular<T>(this T[][] array)
{
    int height = array.Length, width = array[0].Length;
    T[,] rect = new T[height, width];
    for (int i = 0; i < height; i++)
    {
        T[] row = array[i];
        for (int j = 0; j < width; j++)
        {
            rect[i, j] = row[j];
        }
    }
    return rect;
}
// fill an existing rectangular array from a jagged array
static void WriteRows<T>(this T[,] array, params T[][] rows)
{
    for (int i = 0; i < rows.Length; i++)
    {
        T[] row = rows[i];
        for (int j = 0; j < row.Length; j++)
        {
            array[i, j] = row[j];
        }
    }
}