Declare a Range relative to the Active Cell with VBA

Like this:

Dim rng as Range
Set rng = ActiveCell.Resize(numRows, numCols)

then read the contents of that range to an array:

Dim arr As Variant
arr = rng.Value
'arr is now a two-dimensional array of size (numRows, numCols)

or, select the range (I don't think that's what you really want, but you ask for this in the question).

rng.Select

There is an .Offset property on a Range class which allows you to do just what you need

ActiveCell.Offset(numRows, numCols)

follow up on a comment:

Dim newRange as Range
Set newRange = Range(ActiveCell, ActiveCell.Offset(numRows, numCols))

and you can verify by MsgBox newRange.Address

and here's how to assign this range to an array