Transposing

When you transpose an array you are swapping the corresponding rows and columns
If you have a (2 x 6) array then its transpose will be a (6 x 2) array
There are a number of ways you can transpose an array in Excel.

Manual Transpose

This function will transpose a 0-based variant array and manually transpose each element,

Public Function TransposeArray(myarray As Variant) As Variant 
Dim X As Long 
Dim Y As Long 
Dim Xupper As Long 
Dim Yupper As Long 
Dim tempArray As Variant 
    Xupper = UBound(myarray, 2) 
    Yupper = UBound(myarray, 1) 
    ReDim tempArray(Xupper, Yupper) 
    For X = 0 To Xupper 
        For Y = 0 To Yupper 
            tempArray(X, Y) = myarray(Y, X) 
        Next Y 
    Next X 
    TransposeArray = tempArray 
End Function 

Excel - Application.WorksheetFunction.Transpose

This function can also be called using the shorthand Application.Transpose.
This does not appear in intellisense because it is only available for backwards compatibility.
When you use this worksheet function on a worksheet you must enter the function as an array formula in a range.
The number of elements cannot exceed 5461.
The array cannot contain any Null values.
'https://support.microsoft.com/en-gb/help/177991/xl-limitations-of-passing-arrays-to-excel-using-automation
The array cannot contain any items longer than 255 characters.

These can generate one the following errors:
13, Type Mismatch
5, Invalid procedure call or argument
1004, application defined or object defined error.

Excel - Retrieve, Modify and Paste

Lets imagine that we want to take some data from a cell range, modify the contents and then paste the new data back to the worksheet
If you are retrieving data from a worksheet you will always get a 2-dimensional array, even if you only choose a single row or column.
If you step through this code you will see that the array "myarray" is a 2-dimensional array.
It is also very important to emphasise that this array starts at 1 and not 0.
The last line transposes the array and displays it horizontally.

Public Sub RetrieveModifyAndPaste() 
Dim myarray As Variant 
    myarray = Range("A1:A5").Value 
    myarray(2, 1) = "some text" 
    Range("A1:A5").Value = myarray 
    Range("A7:E7").Value = Application.WorksheetFunction.Transpose(myarray) 
End Sub 

Excel - Create and Paste

If you are using lists of data in VBA then you might be working with a 1-dimensional array
If you want to put a 1-dimensional array onto a worksheet then you must transpose the array

Public Sub PasteToWorksheet() 
Dim myarray As Variant 
    myarray = Array(1, 2, 3, 4, 5) 
    Range("C1:C5").Value = Application.WorksheetFunction.Transpose(myarray) 
End Sub 

Excel - Paste Special

One of the optional arguments of the Range.PasteSpecial method is a Transpose value.
The default value is False but setting this value to True lets you easily transpose the contents before pasting them.

Public Sub CopyAndPasteSpecial() 
  Dim sourceRange As Excel.Range 
  Dim targetRange As Excel.Range 
  Set sourceRange = ActiveSheet.Range(Cells(1, 1), Cells(5, 1)) 
  Set targetRange = ActiveSheet.Cells(7, 1) 
  sourceRange.Copy 
  targetRange.PasteSpecial Paste:=xlPasteValues, Operation:=xlNone, SkipBlanks:=False, Transpose:=True 
End Sub 

Important

When transferring a one-dimensional array to a range, the range must be horizontal (i.e. one row with multiple columns).
If you have to use a vertical range instead you must first transpose the array. You can use Excels built in TRANSPOSE() worksheet function to do this.
If you try and transpose an array that contains more than 65535 (2^16) elements then you receive a type mismatch.
Array Formula that try to return more than 65535 rows from a UDF fail with #Value even in Excel 2010.